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Journal articles on the topic 'Hypoellipticité'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 May 2024

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1

Xu, Chaojiang. "Hypoellipticité d'équations aux dérivées partielles non linéaires." Journées équations aux dérivées partielles, no. 1 (1985): 1–16. http://dx.doi.org/10.5802/jedp.299.

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2

Morioka, Tatsushi. "Hypoellipticité pour un certain opérateur à caractéristique double." Tsukuba Journal of Mathematics 21, no. 3 (December 1997): 739–62. http://dx.doi.org/10.21099/tkbjm/1496163378.

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3

Donno, Giuseppe De. "Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity." Tamkang Journal of Mathematics 38, no. 2 (June 30, 2007): 183–89. http://dx.doi.org/10.5556/j.tkjm.38.2007.89.

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The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell's Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor's formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an equivalence for the mentioned H"{o}r-man-der's hypoellipticity conditions.

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4

Bergamasco, Adalberto P., and Sérgio Luís Zani. "Global Hypoellipticity of a Class of Second Order Operators." Canadian Mathematical Bulletin 37, no. 3 (September 1, 1994): 301–5. http://dx.doi.org/10.4153/cmb-1994-045-4.

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AbstractWe show that almost all perturbations P — λ, λ € C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values λ € C for which the operator is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.

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5

Nedeljkov, M., and S. Pilipović. "Hypoelliptic differential operators with generalized constant coefficients." Proceedings of the Edinburgh Mathematical Society 41, no. 1 (February 1998): 47–60. http://dx.doi.org/10.1017/s0013091500019428.

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The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

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6

Himonas, A. Alexandrou. "analytic hypoellipticity." Duke Mathematical Journal 59, no. 1 (August 1989): 265–87. http://dx.doi.org/10.1215/s0012-7094-89-05909-7.

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7

Street, Brian. "What is ...Hypoellipticity?" Notices of the American Mathematical Society 65, no. 04 (April 1, 2018): 1. http://dx.doi.org/10.1090/noti1670.

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8

Bergamasco, A. P., G. A. Mendoza, and S. Zani. "On Global Hypoellipticity." Communications in Partial Differential Equations 37, no. 9 (March 29, 2012): 1517–27. http://dx.doi.org/10.1080/03605302.2011.641054.

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9

Nedeljkov, Marko, and Stevan Pilipovic. "On hypoellipticity in ς." Bulletin: Classe des sciences mathematiques et natturalles 123, no. 27 (2002): 47–56. http://dx.doi.org/10.2298/bmat0227047n.

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We give a condition of sufficiency for the hypoellipticity of a family of equations with constant coefficients satisfied prescribed power growth rate with respect to ? ? (0, 1). The framework is Colombeau algebra of generalized functions.

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10

Street, Brian. "WHAT ELSE about...Hypoellipticity?" Notices of the American Mathematical Society 65, no. 04 (April 1, 2018): 1. http://dx.doi.org/10.1090/noti1664.

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11

Cordaro, Paulo D., and Nicholas Hanges. "Hyperfunctions and (analytic) hypoellipticity." Mathematische Annalen 344, no. 2 (November 28, 2008): 329–39. http://dx.doi.org/10.1007/s00208-008-0308-2.

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12

Yoshino, Masafumi. "Global hypoellipticity and continued fractions." Tsukuba Journal of Mathematics 15, no. 1 (June 1991): 193–203. http://dx.doi.org/10.21099/tkbjm/1496161581.

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13

Morimoto, Yoshinori. "On a criterion for hypoellipticity." Proceedings of the Japan Academy, Series A, Mathematical Sciences 62, no. 4 (1986): 137–40. http://dx.doi.org/10.3792/pjaa.62.137.

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14

Morimoto, Yoshinori, and Chao-Jiang Xu. "Nonlinear Hypoellipticity of Infinite Type." Funkcialaj Ekvacioj 50, no. 1 (2007): 33–65. http://dx.doi.org/10.1619/fesi.50.33.

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15

Bergamasco, Adalberto P. "Remarks about global analytic hypoellipticity." Transactions of the American Mathematical Society 351, no. 10 (March 19, 1999): 4113–26. http://dx.doi.org/10.1090/s0002-9947-99-02299-0.

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16

Petersen, Johannes A. "Hypoellipticity on Cauchy-Riemann manifolds." Transactions of the American Mathematical Society 334, no. 2 (February 1, 1992): 615–39. http://dx.doi.org/10.1090/s0002-9947-1992-1113696-6.

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17

Chanillo, Sagun, Bernard Helffer, and Ari Laptev. "Nonlinear eigenvalues and analytic hypoellipticity." Journal of Functional Analysis 209, no. 2 (April 2004): 425–43. http://dx.doi.org/10.1016/s0022-1236(03)00105-8.

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18

Yu, Ching-Chau. "Nonlinear eigenvalues and analytic-hypoellipticity." Memoirs of the American Mathematical Society 134, no. 636 (1998): 0. http://dx.doi.org/10.1090/memo/0636.

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19

Matsuzawa, Tadato. "Gevrey hypoellipticity for Grushin operators." Publications of the Research Institute for Mathematical Sciences 33, no. 5 (1997): 775–99. http://dx.doi.org/10.2977/prims/1195145017.

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20

Takei, Yoshitsugu. "A fine microlocalization and hypoellipticity." Journal of Mathematics of Kyoto University 29, no. 1 (1989): 127–57. http://dx.doi.org/10.1215/kjm/1250520311.

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21

Ninomiya, Haruki. "On a problem of hypoellipticity." Journal of Mathematics of Kyoto University 27, no. 4 (1987): 587–95. http://dx.doi.org/10.1215/kjm/1250520600.

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22

Christ, Michael. "Examples pertaining to Gevrey hypoellipticity." Mathematical Research Letters 4, no. 5 (1997): 725–33. http://dx.doi.org/10.4310/mrl.1997.v4.n5.a10.

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23

Aragão-Costa, E. R. "Local Hypoellipticity by Lyapunov Function." Abstract and Applied Analysis 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7210540.

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We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators:Lj=∂/∂tj+(∂ϕ/∂tj)(t,A)A,j=1,2,…,n, whereA:D(A)⊂H→His a self-adjoint linear operator, positive with0∈ρ(A), in a Hilbert spaceH, andϕ=ϕ(t,A)is a series of nonnegative powers ofA-1with coefficients inC∞(Ω),Ωbeing an open set ofRn, for anyn∈N, different from what happens in the work of Hounie (1979) who studies the problem only in the casen=1. We provide sufficient condition to get the local hypoellipticity for that complex in the elliptic region, using a Lyapunov function and the dynamics properties of solutions of the Cauchy problemt′(s)=-∇Reϕ0(t(s)),s≥0,t(0)=t0∈Ω,ϕ0:Ω→Cbeing the first coefficient ofϕ(t,A). Besides, to get over the problem out of the elliptic region, that is, in the pointst∗ ∈Ωsuch that∇Reϕ0(t∗)= 0, we will use the techniques developed by Bergamasco et al. (1993) for the particular operatorA=1-Δ:H2(RN)⊂L2(RN)→L2(RN).

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24

Himonas, A. Alexandrou, and Gerson Petronilho. "Global Hypoellipticity and Simultaneous Approximability." Journal of Functional Analysis 170, no. 2 (February 2000): 356–65. http://dx.doi.org/10.1006/jfan.1999.3524.

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25

Xuebo, Luo. "Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators." Canadian Journal of Mathematics 46, no. 1 (February 1, 1994): 212–24. http://dx.doi.org/10.4153/cjm-1994-008-1.

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AbstractIn this paper the Corwin's conjecture is proved, which says that if d is a function analytic near ∞, then the hypoellipticity of the convolution operator Ad, defined by for every u ∊ S'(ℝn), implies that P(x)/ logx → ∞ as x → ∞, where P(x) is the distance from x ∊ ℝn to the set of complex zeros of d.

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26

Morimoto, Yoshinori. "Criteria for hypoellipticity of differential operators." Publications of the Research Institute for Mathematical Sciences 22, no. 6 (1986): 1129–54. http://dx.doi.org/10.2977/prims/1195177066.

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27

Morimoto, Yoshinori. "Non-hypoellipticity for degenerate elliptic operators." Publications of the Research Institute for Mathematical Sciences 22, no. 1 (1986): 25–30. http://dx.doi.org/10.2977/prims/1195178369.

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28

Margaryan, V. N. "Comparison of polynomials and almost hypoellipticity." Journal of Contemporary Mathematical Analysis 47, no. 1 (February 2012): 16–27. http://dx.doi.org/10.3103/s1068362312010025.

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29

Bergamasco, Adalberto P., and Edna M. Zuffi. "On global hypoellipticity on the torus." Tsukuba Journal of Mathematics 21, no. 2 (October 1997): 319–27. http://dx.doi.org/10.21099/tkbjm/1496163244.

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30

Bove, Antonio, and David S. Tartakoff. "Gevrey Hypoellipticity for Non-subelliptic Operators." Pure and Applied Mathematics Quarterly 6, no. 3 (2010): 663–76. http://dx.doi.org/10.4310/pamq.2010.v6.n3.a2.

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31

Chinni, Gregorio. "Germ hypoellipticity and loss of derivatives." Proceedings of the American Mathematical Society 140, no. 7 (July 1, 2012): 2417–27. http://dx.doi.org/10.1090/s0002-9939-2011-11252-8.

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32

Himonas, A. Alexandrou, and Gerson Pentronilho. "Propagation of regularity and global hypoellipticity." Michigan Mathematical Journal 50, no. 3 (2002): 471–82. http://dx.doi.org/10.1307/mmj/1039029977.

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33

Yoshino, Masafumi. "Global hypoellipticity of a Mathieu operator." Proceedings of the American Mathematical Society 111, no. 3 (March 1, 1991): 717. http://dx.doi.org/10.1090/s0002-9939-1991-1042277-2.

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34

Mughetti, Marco. "Hypoellipticity and higher order Levi conditions." Journal of Differential Equations 257, no. 4 (August 2014): 1246–87. http://dx.doi.org/10.1016/j.jde.2014.05.008.

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35

Mannucci, Paola, and Bianca Stroffolini. "Periodic homogenization under a hypoellipticity condition." Nonlinear Differential Equations and Applications NoDEA 22, no. 4 (November 14, 2014): 579–600. http://dx.doi.org/10.1007/s00030-014-0296-8.

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36

Koenig, Kenneth D. "Maximal hypoellipticity for the ∂¯-Neumann problem." Advances in Mathematics 282 (September 2015): 128–219. http://dx.doi.org/10.1016/j.aim.2015.06.013.

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37

Kazaryan, G. G. "ON A FUNCTIONAL INDEX OF HYPOELLIPTICITY." Mathematics of the USSR-Sbornik 56, no. 2 (February 28, 1987): 333–47. http://dx.doi.org/10.1070/sm1987v056n02abeh003039.

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38

Christ, Michael. "A Necessary Condition For Analytic Hypoellipticity." Mathematical Research Letters 1, no. 2 (1994): 241–48. http://dx.doi.org/10.4310/mrl.1994.v1.n2.a11.

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39

ALEXANDRE, R. "FRACTIONAL ORDER KINETIC EQUATIONS AND HYPOELLIPTICITY." Analysis and Applications 10, no. 03 (July 2012): 237–47. http://dx.doi.org/10.1142/s021953051250011x.

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We give simple proofs of hypoelliptic estimates for some models of kinetic equations with a fractional order diffusion part. The proofs are based on energy estimates together with the previous ideas of Bouchut and Perthame.

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40

Li, Wei-Xi, and Alberto Parmeggiani. "Global Gevrey hypoellipticity for twisted Laplacians." Journal of Pseudo-Differential Operators and Applications 4, no. 3 (May 25, 2013): 279–96. http://dx.doi.org/10.1007/s11868-013-0073-1.

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41

Herzog, David P., and Nathan Totz. "An Extension of Hörmander’s Hypoellipticity Theorem." Potential Analysis 42, no. 2 (September 21, 2014): 403–33. http://dx.doi.org/10.1007/s11118-014-9439-0.

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42

Kohn, J. J. "Hypoellipticity of Some Degenerate Subelliptic Operators." Journal of Functional Analysis 159, no. 1 (October 1998): 203–16. http://dx.doi.org/10.1006/jfan.1998.3289.

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43

Kirilov, Alexandre, and Wagner A. A. de Moraes. "Global hypoellipticity for strongly invariant operators." Journal of Mathematical Analysis and Applications 486, no. 1 (June 2020): 123878. http://dx.doi.org/10.1016/j.jmaa.2020.123878.

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44

Bahri, Mawardi, Ryuichi Ashino, and Rémi Vaillancourt. "Convolution Theorems for Quaternion Fourier Transform: Properties and Applications." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/162769.

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General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

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45

Sibony, Nessim. "Hypoellipticit� pour l'op�rateur $$\bar \partial $$." Mathematische Annalen 276, no. 2 (January 1987): 279–90. http://dx.doi.org/10.1007/bf01450742.

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46

Bell, Denis. "The Malliavin calculus and hypoelliptic differential operators." Infinite Dimensional Analysis, Quantum Probability and Related Topics 18, no. 01 (March 2015): 1550001. http://dx.doi.org/10.1142/s0219025715500010.

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This article is intended as an introduction to Malliavin's stochastic calculus of variations and his probabilistic approach to hypoellipticity. Topics covered include an elementary derivation of the basic integration by parts formulae, a proof of the probabilistic version of Hörmander's theorem as envisioned by Malliavin and completed by Kusuoka and Stroock, and an extension of Hörmander's theorem valid for operators with degeneracy of exponential type due to the author and S. Mohammed.

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47

SHARDLOW, TONY, and YUBIN YAN. "GEOMETRIC ERGODICITY FOR DISSIPATIVE PARTICLE DYNAMICS." Stochastics and Dynamics 06, no. 01 (March 2006): 123–54. http://dx.doi.org/10.1142/s0219493706001670.

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Dissipative particle dynamics is a model of multi-phase fluid flows described by a system of stochastic differential equations. We consider the problem of N particles evolving on the one-dimensional periodic domain of length L and, if the density of particles is large, prove geometric convergence to a unique invariant measure. The proof uses minorization and drift arguments, but allows elements of the drift and diffusion matrix to have compact support, in which case hypoellipticity arguments are not directly available.

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48

Chen, So-Chin. "Global analytic hypoellipticity of □bon circular domains." Pacific Journal of Mathematics 175, no. 1 (September 1, 1996): 61–70. http://dx.doi.org/10.2140/pjm.1996.175.61.

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49

Francsics, G�bor. "Hypoellipticity in the tangential Cauchy-Riemann complex." Duke Mathematical Journal 73, no. 1 (January 1994): 25–77. http://dx.doi.org/10.1215/s0012-7094-94-07302-x.

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50

Christ, Michael. "Examples of analytic non-hypoellipticity of ∂b." Communications in Partial Differential Equations 19, no. 5-6 (January 1994): 911–41. http://dx.doi.org/10.1080/03605309408821040.

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