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Journal articles on the topic 'Baouendi-Grushin operator'

Author: Grafiati

Published: 25 May 2024

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1

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 (October 19, 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 are also obtained.

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2

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 strong unique continuation property for a class of degenerate sublinear equations. We also derive a subelliptic version of a scaling critical Carleman estimate proven by Regbaoui in the Euclidean setting using which we deduce a new unique continuation result in the case of scaling critical Hardy type potentials.</p>

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3

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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4

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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5

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 (March 8, 2015): 1067–87. http://dx.doi.org/10.1007/s00030-015-0314-5.

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6

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 (April 2009): 385–96. http://dx.doi.org/10.1134/s0001434609030092.

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7

Metafune, Giorgio, Luigi Negro, and Chiara Spina. "Lp estimates for Baouendi–Grushin operators." Pure and Applied Analysis 2, no. 3 (November 17, 2020): 603–25. http://dx.doi.org/10.2140/paa.2020.2.603.

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8

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 (April 5, 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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9

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

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10

Garofalo, Nicola, and Dimiter Vassilev. "Strong Unique Continuation Properties of Generalized Baouendi–Grushin Operators." Communications in Partial Differential Equations 32, no. 4 (April 11, 2007): 643–63. http://dx.doi.org/10.1080/03605300500532905.

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11

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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12

Kombe, Ismail, and Abdullah Yener. "Weighted Rellich type inequalities related to Baouendi-Grushin operators." Proceedings of the American Mathematical Society 145, no. 11 (July 10, 2017): 4845–57. http://dx.doi.org/10.1090/proc/13730.

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13

Kombe, Ismail, and Abdullah Yener. "General weighted Hardy type inequalities related to Baouendi-Grushin operators." Complex Variables and Elliptic Equations 63, no. 3 (May 28, 2017): 420–36. http://dx.doi.org/10.1080/17476933.2017.1318128.

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14

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

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15

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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16

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 (July 15, 2011): 1637–44. http://dx.doi.org/10.1007/s10114-011-8212-1.

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17

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 (May 2013): 5167–76. http://dx.doi.org/10.3934/dcds.2013.33.5167.

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18

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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19

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 (October 11, 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 existence of stationary waves by applying the theory of pseudomonotone operators. The analysis carried out in this paper is motivated by patterns arising in the theory of transonic flows.

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20

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 $i\partial _tu-\left (-\Delta _{\gamma }\right )^{s}u=0$ , where $s\in \mathbb N$ . We identify three different cases: depending on the value of the ratio $(\gamma +1)/s$ , observability may hold in arbitrarily small time or only for sufficiently large times or may even fail for any time. As a corollary of our resolvent estimate, we also obtain observability for heat-type equations $\partial _tu+\left (-\Delta _{\gamma }\right )^su=0$ and establish a decay rate for the damped wave equation associated with $\Delta _{\gamma }$ .

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21

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 the parameter. The analysis developed in this paper is associated with patterns describing transonic flow restricted to subsonic regions.

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22

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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23

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 (January 1, 2023). http://dx.doi.org/10.57262/ade028-0102-143.

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24

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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