Relevant bibliographies by topics / Morrey spaces,integral operators,partial differential equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Morrey spaces,integral operators,partial differential equations'

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Published: 21 February 2023

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Journal articles on the topic "Morrey spaces,integral operators,partial differential equations"

1

Ragusa, Maria Alessandra, and Veli Shakhmurov. "Embedding of vector-valued Morrey spaces and separable differential operators." Bulletin of Mathematical Sciences 09, no. 02 (August 2019): 1950013. http://dx.doi.org/10.1142/s1664360719500139.

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The paper is the first part of a program devoted to the study of the behavior of operator-valued multipliers in Morrey spaces. Embedding theorems and uniform separability properties involving [Formula: see text]-valued Morrey spaces are proved. As a consequence, maximal regularity for solutions of infinite systems of anisotropic elliptic partial differential equations are established.
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2

Wang, Jiajia, Zunwei Fu, Shaoguang Shi, and Ling Mi. "Operator Inequalities of Morrey Spaces Associated with Karamata Regular Variation." Journal of Function Spaces 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/4618197.

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Karamata regular variation is a basic tool in stochastic process and the boundary blow-up problems for partial differential equations (PDEs). Morrey space is closely related to study of the regularity of solutions to elliptic PDEs. The aim of this paper is trying to bring together these two areas and this paper is intended as an attempt at motivating some further research on these areas. A version of Morrey space associated with Karamata regular variation is introduced. As application, some estimates of operators, especially one-sided operators, on these spaces are considered.
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3

Hasanov, Javanshir J., Rabil Ayazoglu, and Simten Bayrakci. "B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces." Open Mathematics 18, no. 1 (July 10, 2020): 715–30. http://dx.doi.org/10.1515/math-2020-0033.

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Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .
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4

Fedorov, V. E., A. D. Godova, and B. T. Kien. "Integro-differential equations with bounded operators in Banach spaces." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 106, no. 2 (June 30, 2022): 93–107. http://dx.doi.org/10.31489/2022m2/93-107.

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The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann—Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also include those in which the convolution has an integral kernel without singularities. The conditions of the unique solvability of the Cauchy type problem for a linear integro-differential equation of the Riemann—Liouville type and the Cauchy problem for a linear integrodifferential equation of the Gerasimov type with a bounded operator at the unknown function are obtained. These results are used in the study of similar equations with a degenerate operator at an integro-differential operator under the condition of relative boundedness of the pair of operators from the equation. Abstract results are applied to the study of initial boundary value problems for partial differential equations with an integro-differential operator, the convolution in which is given by the Mittag-Leffler function multiplied by a power function.
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Nguyen, Thieu Huy, Vu Thi Ngoc Ha, and Trinh Xuan Yen. "Admissible integral manifolds for partial neutral functional-differential equations." Ukrains’kyi Matematychnyi Zhurnal 74, no. 10 (November 27, 2022): 1364–87. http://dx.doi.org/10.37863/umzh.v74i10.6257.

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UDC 517.9 We prove the existence and attraction property for admissible invariant unstable and center-unstable manifolds of admissible classes of solutions to the partial neutral functional-differential equation in Banach space X of the form & ∂ ∂ t F u t = A ( t ) F u t + f ( t , u t ) , t ≥ s , t , s ∈ ℝ , & u s = ϕ ∈ 𝒞 : = C ( [ - r ,0 ] , X ) under the conditions that the family of linear partial differential operators ( A ( t ) ) t ∈ ℝ generates the evolution family ( U ( t , s ) ) t ≥ s with an exponential dichotomy on the whole line ℝ ; the difference operator F : 𝒞 → X is bounded and linear, and the nonlinear delay operator f satisfies the φ -Lipschitz condition, i.e., ‖ f ( t , ϕ ) - f ( t , ψ ) ‖ ≤ φ ( t ) ‖ ϕ - ψ ‖ 𝒞 for ϕ , ψ ∈ 𝒞 , where φ ( ⋅ ) belongs to an admissible function space defined on ℝ . We also prove that an unstable manifold of the admissible class attracts all other solutions with exponential rates. Our main method is based on the Lyapunov – Perron equation combined with the admissibility of function spaces. We apply our results to the finite-delayed heat equation for a material with memory.
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6

CHKADUA, O., S. E. MIKHAILOV, and D. NATROSHVILI. "ANALYSIS OF DIRECT SEGREGATED BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVPs IN EXTERIOR DOMAINS." Analysis and Applications 11, no. 04 (June 18, 2013): 1350006. http://dx.doi.org/10.1142/s0219530513500061.

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Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.
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7

Providas, Efthimios, and Ioannis Nestorios Parasidis. "A Procedure for Factoring and Solving Nonlocal Boundary Value Problems for a Type of Linear Integro-Differential Equations." Algorithms 14, no. 12 (November 28, 2021): 346. http://dx.doi.org/10.3390/a14120346.

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The aim of this article is to present a procedure for the factorization and exact solution of boundary value problems for a class of n-th order linear Fredholm integro-differential equations with multipoint and integral boundary conditions. We use the theory of the extensions of linear operators in Banach spaces and establish conditions for the decomposition of the integro-differential operator into two lower-order integro-differential operators. We also create solvability criteria and derive the unique solution in closed form. Two example problems for an ordinary and a partial intergro-differential equation respectively are solved.
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8

Chen, Jiao, Wei Ding, and Guozhen Lu. "Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces." Forum Mathematicum 32, no. 4 (July 1, 2020): 919–36. http://dx.doi.org/10.1515/forum-2019-0319.

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AbstractAfter the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are {L^{p}({\mathbb{R}^{n}})} bounded for {1<p<\infty}, but only bounded on local Hardy spaces {h^{p}({\mathbb{R}^{n}})} introduced by Goldberg in [D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 1979, 1, 27–42] for {0<p\leq 1}. Though much work has been done on the {L^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {1<p<\infty} and Hardy {H^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {0<p\leq 1} for multi-parameter Fourier multipliers and singular integral operators, not much has been done yet for the boundedness of multi-parameter pseudo-differential operators in the range of {0<p\leq 1}. The main purpose of this paper is to establish the boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} for {0<p\leq 1} recently introduced by Ding, Lu and Zhu in [W. Ding, G. Lu and Y. Zhu, Multi-parameter local Hardy spaces, Nonlinear Anal. 184 2019, 352–380].
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Оdinabekov, Jasur M. "On the Noethericity conditions and the index of some two–dimensional singular integral operators." Russian Universities Reports. Mathematics, no. 138 (2022): 164–74. http://dx.doi.org/10.20310/2686-9667-2022-27-138-164-174.

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The main problems in the theory of singular integral operators are the problems of boundedness, invertibility, Noethericity, and calculation of the index. The general theory of multidimensional singular integral operators over the entire space E_n was constructed by S.G. Mikhlin. It is known that in the two-dimensional case, if the symbol of an operator does not vanish, then the Fredholm theory holds. For operators over a bounded domain, the boundary of this domain significantly affects the solvability of the corresponding operator equations. In this paper, we consider two-dimensional singular integral operators with continuous coefficients over a bounded domain. Such operators are used in many problems in the theory of partial differential equations. In this regard, it is of interest to establish criteria for the considered operators to be Noetherian in the form of explicit conditions on their coefficients. The paper establishes effective necessary and sufficient conditions for two-dimensional singular integral operators to be Noetherian in Lebesgue spaces L_p (D) (considered over the field of real numbers), 1<p<∞, and formulas for calculating indices are given. The method developed by R.V. Duduchava [Duduchava R. On multidimensional singular integral operators. I: The half-space case; II: The case of compact manifolds // J. Operator Theory, 1984, v. 11, 41–76 (I); 199–214 (II)]. In this case, the study of the Noetherian properties of operators is reduced to the factorization of the corresponding matrix-functions and finding their partial indices.
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10

Sitnik, Sergey M., Vladimir E. Fedorov, Nikolay V. Filin, and Viktor A. Polunin. "On the Solvability of Equations with a Distributed Fractional Derivative Given by the Stieltjes Integral." Mathematics 10, no. 16 (August 18, 2022): 2979. http://dx.doi.org/10.3390/math10162979.

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Linear equations in Banach spaces with a distributed fractional derivative given by the Stieltjes integral and with a closed operator A in the right-hand side are considered. Unlike the previously studied classes of equations with distributed derivatives, such kinds of equations may contain a continuous and a discrete part of the integral, i.e., a standard integral of the fractional derivative with respect to its order and a linear combination of fractional derivatives with different orders. Resolving families of operators for such equations are introduced into consideration, and their properties are studied. In terms of the resolvent of the operator A, necessary and sufficient conditions are obtained for the existence of analytic resolving families of the equation under consideration. A perturbation theorem for such a class of operators is proved, and the Cauchy problem for the inhomogeneous equation with a distributed fractional derivative is studied. Abstract results are applied for the research of the unique solvability of initial boundary value problems for partial differential equations with a distributed derivative with respect to time.
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Dissertations / Theses on the topic "Morrey spaces,integral operators,partial differential equations"

1

Scapellato, Andrea. "Integral operators and partial differential equations in Morrey type spaces." Doctoral thesis, Università di Catania, 2018. http://hdl.handle.net/10761/4043.

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Lo scopo di questa tesi è lo studio della limitatezza di alcuni operatori integrali in spazi funzionali di tipo Morrey. Inoltre si studia la regolarità di soluzioni di equazioni differenziali alle derivate parziali.
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2

Abdeljawad, Ahmed. "Global microlocal analysis on Rd with applications to hyperbolic partial differential equations and modulation spaces." Doctoral thesis, 2019. http://hdl.handle.net/2318/1718409.

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This thesis treats different aspects of microlocal and time-frequency analysis, with particular emphasis on techniques involving multi-products of Fourier integral operators and one-parameter group properties for pseudodifferential operators. In the first part, we study a class of hyperbolic Cauchy problems, associated with linear operators and systems with polynomially bounded coefficients, variable multiplicities and involutive characteristics, globally defined on Rd. We prove well-posedness in Sobolev-Kato spaces, with loss of smoothness and decay at infinity. We also obtain results about propagation of singularities, in terms of wave-front sets describing the evolution of both smoothness and decay singularities of temperate distributions. In the second part, we deduce lifting property for modulation spaces and construct explicit isomorpisms between them. To prove such results, we study one-parameter group properties for pseudo-differential operators with symbols in some Gevrey-Hörmander classes. Furthermore, we focus on some classes of pseudo-differential operators with symbols admitting anisotropic exponential growth at infinity. We deduce algebraic and invariance properties of these classes. Moreover, we prove mapping properties for these operators on Gelfand-Shilov spaces of type S and modulation spaces.
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Books on the topic "Morrey spaces,integral operators,partial differential equations"

1

Edmunds, David E. Hardy Operators, Function Spaces and Embeddings. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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Spectral theory and geometric analysis: An international conference in honor of Mikhail Shubin's 65th birthday, July 29 - August 2, 2009, Northeastern University, Boston, Massachusetts. Providence, R.I: American Mathematical Society, 2010.

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1980-, Moradifam Amir, ed. Functional inequalities: New perspectives and new applications. Providence, Rhode Island: American Mathematical Society, 2013.

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Jakobson, Dmitry, Pierre Albin, and Frédéric Rochon. Geometric and spectral analysis. Providence, Rhode Island: American Mathematical Society, 2014.

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Mass.) AMS Special Session on Radon Transforms and Geometric Analysis (2012 Boston. Geometric analysis and integral geometry: AMS special session in honor of Sigurdur Helgason's 85th birthday, radon transforms and geometric analysis, January 4-7, 2012, Boston, MA ; Tufts University Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces, January 8-9, 2012, Medford, MA. Edited by Quinto, Eric Todd, 1951- editor of compilation, Gonzalez, Fulton, 1956- editor of compilation, Christensen, Jens Gerlach, 1975- editor of compilation, and Tufts University. Workshop on Geometric Analysis on Euclidean and Homogeneous Spaces. Providence, Rhode Island: American Mathematical Society, 2013.

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Book chapters on the topic "Morrey spaces,integral operators,partial differential equations"

1

Taheri, Ali. "Singular Integral Operators and Vector-Valued Inequalities." In Function Spaces and Partial Differential Equations, 645–700. Oxford University Press, 2015. http://dx.doi.org/10.1093/acprof:oso/9780198733157.003.0016.

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Journal articles
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