Singular subelliptic equations and Sobolev inequalities on Carnot groups

Prashanta Garain; Alexander Ukhlov

doi:10.1007/s13324-022-00676-8

Singular subelliptic equations and Sobolev inequalities on Carnot groups

Prashanta Garain, Alexander Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on Carnot groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q< 1 , 1 < p< ν.

Original language	English
Article number	67
Journal	Analysis and Mathematical Physics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s13324-022-00676-8
State	Published - 1 Apr 2022

Keywords

Carnot groups
Singular problem
Sobolev inequality
Subelliptic operators

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-022-00676-8

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abstract = "In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on Carnot groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q< 1 , 1 < p< ν.",

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N2 - In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on Carnot groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q< 1 , 1 < p< ν.

AB - In this article we study singular subelliptic p-Laplace equations and best constants in Sobolev inequalities on Carnot groups. We prove solvability of these subelliptic p-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding (q, p)-Sobolev inequality, 0 < q< 1 , 1 < p< ν.

KW - Carnot groups

KW - Singular problem

KW - Sobolev inequality

KW - Subelliptic operators

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ER -

Singular subelliptic equations and Sobolev inequalities on Carnot groups

Abstract

Keywords

ASJC Scopus subject areas

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