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Journal articles on the topic 'Baouendi-Grushin operator'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Zhangirbayev, A. "HARDY INEQUALITIES AND IDENTITIES RELATED TO THE BAOUENDI-GRUSHIN VECTOR FIELDS AND LANDAU-HAMILTONIAN." Herald of the Kazakh-British technical university 21, no. 4 (2024): 153–67. https://doi.org/10.55452/1998-6688-2024-21-4-153-167.

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In this paper, we present a weighted Hardy identity related to the Baouendi-Grushin vector fields and its applications in the context of differential inequalities. By selecting appropriate parameters, the Hardy identity related to the Baouendi-Grushin operator implies numerous sharp remainder formulae for Hardy type inequalities. In the commutative case, we obtain improved weighted Hardy inequalities in the setting of the Euclidean space. For example, in a special case, by dropping non-negative remainder terms, related to the Baouendi-Grushin operator, and choosing suitable parameters our iden

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2

Laptev, Ari, Michael Ruzhansky, and Nurgissa Yessirkegenov. "Hardy inequalities for Landau Hamiltonian and for Baouendi-Grushin operator with Aharonov-Bohm type magnetic field. Part I." MATHEMATICA SCANDINAVICA 125, no. 2 (2019): 239–69. http://dx.doi.org/10.7146/math.scand.a-114892.

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In this paper we prove the Hardy inequalities for the quadratic form of the Laplacian with the Landau Hamiltonian type magnetic field. Moreover, we obtain a Poincaré type inequality and inequalities with more general families of weights. Furthermore, we establish weighted Hardy inequalities for the quadratic form of the magnetic Baouendi-Grushin operator for the magnetic field of Aharonov-Bohm type. For these, we show refinements of the known Hardy inequalities for the Baouendi-Grushin operator involving radial derivatives in some of the variables. The corresponding uncertainty type principles

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3

Banerjee, Agnid, and Ramesh Manna. "Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation." Discrete & Continuous Dynamical Systems 41, no. 11 (2021): 5105. http://dx.doi.org/10.3934/dcds.2021070.

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<p style='text-indent:20px;'>In this paper, we obtain new Carleman estimates for a class of variable coefficient degenerate elliptic operators whose constant coefficient model at one point is the so called Baouendi-Grushin operator. This generalizes the results obtained by the two of us with Garofalo in [<xref ref-type="bibr" rid="b10">10</xref>] where similar estimates were established for the "constant coefficient" Baouendi-Grushin operator. Consequently, we obtain: (ⅰ) a Bourgain-Kenig type quantitative uniqueness result in the variable coefficient setting; (ⅱ) and a stron

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4

Bahrouni, Anouar, Vicenţiu D. Rădulescu, and Dušan D. Repovš. "Nonvariational and singular double phase problems for the Baouendi-Grushin operator." Journal of Differential Equations 303 (December 2021): 645–66. http://dx.doi.org/10.1016/j.jde.2021.09.033.

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5

Bahrouni, Anouar, and Vicenţiu D. Rădulescu. "Singular double-phase systems with variable growth for the Baouendi-Grushin operator." Discrete & Continuous Dynamical Systems 41, no. 9 (2021): 4283. http://dx.doi.org/10.3934/dcds.2021036.

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6

Mihăilescu, Mihai, Denisa Stancu-Dumitru, and Csaba Varga. "On the spectrum of a Baouendi–Grushin type operator: an Orlicz–Sobolev space setting approach." Nonlinear Differential Equations and Applications NoDEA 22, no. 5 (2015): 1067–87. http://dx.doi.org/10.1007/s00030-015-0314-5.

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7

Markasheva, V. A., and A. F. Tedeev. "Local and global estimates of the solutions of the Cauchy problem for quasilinear parabolic equations with a nonlinear operator of Baouendi-Grushin type." Mathematical Notes 85, no. 3-4 (2009): 385–96. http://dx.doi.org/10.1134/s0001434609030092.

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8

Metafune, Giorgio, Luigi Negro, and Chiara Spina. "Lp estimates for Baouendi–Grushin operators." Pure and Applied Analysis 2, no. 3 (2020): 603–25. http://dx.doi.org/10.2140/paa.2020.2.603.

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9

Jia, Xiaobiao, and Shanshan Ma. "Holder estimates and asymptotic behavior for degenerate elliptic equations in the half space." Electronic Journal of Differential Equations 2023, no. 01-37 (2023): 33. http://dx.doi.org/10.58997/ejde.2023.33.

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In this article we investigate the asymptotic behavior at infinity of viscosity solutions to degenerate elliptic equations. We obtain Holder estimates, up to the flat boundary, by using the rescaling method. Also as a byproduct we obtain a Liouville type result on Baouendi-Grushin type operators.

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10

Kombe, Ismail. "Nonlinear degenerate parabolic equations for Baouendi–Grushin operators." Mathematische Nachrichten 279, no. 7 (2006): 756–73. http://dx.doi.org/10.1002/mana.200310391.

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11

Garofalo, Nicola, and Dimiter Vassilev. "Strong Unique Continuation Properties of Generalized Baouendi–Grushin Operators." Communications in Partial Differential Equations 32, no. 4 (2007): 643–63. http://dx.doi.org/10.1080/03605300500532905.

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12

Niu, Pengcheng, and Jingbo Dou. "Hardy-Sobolev type inequalities for generalized Baouendi-Grushin operators." Miskolc Mathematical Notes 8, no. 1 (2007): 73. http://dx.doi.org/10.18514/mmn.2007.142.

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13

Kombe, Ismail, and Abdullah Yener. "Weighted Rellich type inequalities related to Baouendi-Grushin operators." Proceedings of the American Mathematical Society 145, no. 11 (2017): 4845–57. http://dx.doi.org/10.1090/proc/13730.

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14

Kombe, Ismail, and Abdullah Yener. "General weighted Hardy type inequalities related to Baouendi-Grushin operators." Complex Variables and Elliptic Equations 63, no. 3 (2017): 420–36. http://dx.doi.org/10.1080/17476933.2017.1318128.

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15

NIU, PENGCHENG, YANXIA CHEN, and YAZHOU HAN. "SOME HARDY-TYPE INEQUALITIES FOR THE GENERALIZED BAOUENDI-GRUSHIN OPERATORS." Glasgow Mathematical Journal 46, no. 3 (2004): 515–27. http://dx.doi.org/10.1017/s0017089504002034.

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16

Chen, Hua, and Xin Liao. "Liouville theorem for Lane-Emden equation of Baouendi-Grushin operators." Journal of Differential Equations 430 (June 2025): 113201. https://doi.org/10.1016/j.jde.2025.02.072.

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17

TANIGUCHI, Setsuo. "AN APPLICATION OF THE PARTIAL MALLIAVIN CALCULUS TO BAOUENDI-GRUSHIN OPERATORS." Kyushu Journal of Mathematics 73, no. 2 (2019): 417–31. http://dx.doi.org/10.2206/kyushujm.73.417.

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18

Wang, Jia Lin, and Peng Cheng Niu. "Unique continuation properties for generalized Baouendi-Grushin operators with singular weights." Acta Mathematica Sinica, English Series 27, no. 8 (2011): 1637–44. http://dx.doi.org/10.1007/s10114-011-8212-1.

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19

Kombe, Ismail. "On the nonexistence of positive solutions to doubly nonlinear equations for Baouendi-Grushin operators." Discrete and Continuous Dynamical Systems 33, no. 11/12 (2013): 5167–76. http://dx.doi.org/10.3934/dcds.2013.33.5167.

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20

Liu, Hairong, and Xiaoping Yang. "Strong unique continuation property for fourth order Baouendi-Grushin type subelliptic operators with strongly singular potential." Journal of Differential Equations 385 (March 2024): 57–85. http://dx.doi.org/10.1016/j.jde.2023.12.002.

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21

Dukenbayeva, Aishabibi. "Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator." Open Mathematics 23, no. 1 (2025). https://doi.org/10.1515/math-2025-0144.

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Abstract In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity argument and the Poincaré inequality related to the Baouendi-Grushin operator from [Suragan and Yessirkegenov, Sharp remainder of the Poincaré inequality for Baouendi–Grushin vector fields, Asian-Eur. J. Math. 16 (2023), 2350041], inspired by the recent work [Ruzhansky et al., Global existence and blow-up of solutions to porous medium equation and pseudo

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22

Hillairet, Luc, and Mohammad Harakeh. "A spectral condition for the control of eigenfunctions of Baouendi-Grushin type operators." ESAIM: Control, Optimisation and Calculus of Variations, April 29, 2025. https://doi.org/10.1051/cocv/2025042.

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Abstract. We prove a generic simplicity result on the multiplicity of the eigenvalues of the generalized Baouendi Grushin operator that implies the validity of concentration inequality for eigenfunctions.

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23

Li, Huaiqian, and Ke Wang. "Dimension-free Maz’ya–Shaposhnikova limiting formulas in Grushin spaces." Rendiconti Lincei, Matematica e Applicazioni, May 6, 2025. https://doi.org/10.4171/rlm/1054.

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Motivated by the paper [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXIII (2022) 837–875], we provide a simplified and robust proof of the dimension-free Maz’ya–Shaposhnikova limiting formula for seminorms associated with the Baouendi–Grushin operator. This operator, which is generally non-hypoelliptic, arises frequently in the study of Carnot–Carathéodory spaces. Our approach not only streamlines the original argument but also extends a recent result from [arXiv:2401.03409].

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24

Bahrouni, Anouar, Vicenţiu D. Rădulescu, and Patrick Winkert. "Double phase problems with variable growth and convection for the Baouendi–Grushin operator." Zeitschrift für angewandte Mathematik und Physik 71, no. 6 (2020). http://dx.doi.org/10.1007/s00033-020-01412-7.

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AbstractIn this paper we study a class of quasilinear elliptic equations with double phase energy and reaction term depending on the gradient. The main feature is that the associated functional is driven by the Baouendi–Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. We first establish some new qualitative properties of a differential operator introduced recently by Bahrouni et al. (Nonlinearity 32(7):2481–2495, 2019). Next, under quite general assumptions on the convection term, we prove the ex

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25

Letrouit, Cyril, and Chenmin Sun. "OBSERVABILITY OF BAOUENDI–GRUSHIN-TYPE EQUATIONS THROUGH RESOLVENT ESTIMATES." Journal of the Institute of Mathematics of Jussieu, June 14, 2021, 1–39. http://dx.doi.org/10.1017/s1474748021000207.

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Abstract In this article, we study the observability (or equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed of propagation of these equations, notably in the ‘degenerated directions’ of the subelliptic structure. First, for any $\gamma \geq 1$ , we establish a resolvent estimate for the Baouendi–Grushin-type operator $\Delta _{\gamma }=\partial _x^2+\left \lvert x\right \rvert ^{2\gamma }\partial _y^2$ , which has step $\gamma +1$ . We then derive consequences for the observability of the Schrödinger-type equation $

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26

Alsaedi, Ahmed, Vicenţiu D. Rădulescu, and Bashir Ahmad. "Bifurcation analysis for degenerate problems with mixed regime and absorption." Bulletin of Mathematical Sciences, July 4, 2020, 2050017. http://dx.doi.org/10.1142/s1664360720500174.

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We are concerned with the study of a bifurcation problem driven by a degenerate operator of Baouendi–Grushin type. Due to its degenerate structure, this differential operator has a mixed regime. Studying the combined effects generated by the absorption and the reaction terms, we establish the bifurcation behavior in two cases. First, if the absorption nonlinearity is dominating, then the problem admits solutions only for high perturbations of the reaction. In the case when the reaction dominates the absorption term, we prove that the problem admits nontrivial solutions for all the values of th

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27

Arnaiz, Victor, and Chenmin Sun. "Sharp Resolvent Estimate for the Damped-Wave Baouendi–Grushin Operator and Applications." Communications in Mathematical Physics, January 7, 2023. http://dx.doi.org/10.1007/s00220-022-04606-4.

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28

Jleli, Mohamed, Maria Alessandra Ragusa, and Bessem Samet. "Nonlinear Liouville-type theorems for generalized Baouendi-Grushin operator on Riemannian manifolds." Advances in Differential Equations 28, no. 1/2 (2023). http://dx.doi.org/10.57262/ade028-0102-143.

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29

Jleli, Mohamed, and Bessem Samet. "Nonlinear Liouville-type theorem for a differential inequality involving Dunkl-Baouendi-Grushin operator." Discrete and Continuous Dynamical Systems - S, 2024, 0. http://dx.doi.org/10.3934/dcdss.2024087.

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30

Ruzhansky, Michael, and Bolys Sabitbek. "Hardy and Rellich Inequalities with Bessel Pairs." Proceedings of the Edinburgh Mathematical Society, March 31, 2025, 1–18. https://doi.org/10.1017/s0013091524000051.

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Abstract In this paper, we establish suitable characterisations for a pair of functions $(W(x),H(x))$ on a bounded, connected domain $\Omega \subset \mathbb{R}^n$ in order to have the following Hardy inequality: \begin{equation*} \int_{\Omega} W(x) |\nabla u|_A^2 dx \geq \int_{\Omega} |\nabla d|^2_AH(x)|u|^2 dx, \,\,\, u \in C^{1}_0(\Omega), \end{equation*} where d(x) is a suitable quasi-norm (gauge), $|\xi|^2_A = \langle A(x)\xi, \xi \rangle$ for $\xi \in \mathbb{R}^n$ and A(x) is an n × n symmetric, uniformly positive definite matrix defined on a bounded domain $\Omega \subset \mathbb{R}^n$

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31

Banerjee, Agnid, Nicola Garofalo, and Ramesh Manna. "Carleman estimates for Baouendi–Grushin operators with applications to quantitative uniqueness and strong unique continuation." Applicable Analysis, January 29, 2020, 1–22. http://dx.doi.org/10.1080/00036811.2020.1713314.

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