Weighted and anisotropic Sobolev inequality with extremal

Kaushik Bal; Prashanta Garain

doi:10.1007/s00229-021-01298-3

Weighted and anisotropic Sobolev inequality with extremal

Kaushik Bal, Prashanta Garain

Department of Mathematics

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

8 Scopus citations

Abstract

For a bounded smooth domain Ω ⊂ R^N with N≥ 2 , we establish a weighted and an anisotropic version of Sobolev inequality related to the embedding W01,p(Ω)↪Lq(Ω) for 1 < p< ∞ and 2 ≤ p< ∞ respectively. Our main emphasize is the case of 0 < q< 1 and we deal with a class of Muckenhoupt weights. Moreover, we obtain existence results for weighted and anisotropic p-Laplace equation with mixed singular nonlinearities and observe that the extremals of our inequalities are associated to such singular problems.

Original language	English
Pages (from-to)	101-117
Number of pages	17
Journal	Manuscripta Mathematica
Volume	168
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-021-01298-3
State	Published - 1 May 2022

ASJC Scopus subject areas

General Mathematics

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abstract = "For a bounded smooth domain Ω ⊂ RN with N≥ 2 , we establish a weighted and an anisotropic version of Sobolev inequality related to the embedding W01,p(Ω)↪Lq(Ω) for 1 < p< ∞ and 2 ≤ p< ∞ respectively. Our main emphasize is the case of 0 < q< 1 and we deal with a class of Muckenhoupt weights. Moreover, we obtain existence results for weighted and anisotropic p-Laplace equation with mixed singular nonlinearities and observe that the extremals of our inequalities are associated to such singular problems.",

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AU - Garain, Prashanta

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AB - For a bounded smooth domain Ω ⊂ RN with N≥ 2 , we establish a weighted and an anisotropic version of Sobolev inequality related to the embedding W01,p(Ω)↪Lq(Ω) for 1 < p< ∞ and 2 ≤ p< ∞ respectively. Our main emphasize is the case of 0 < q< 1 and we deal with a class of Muckenhoupt weights. Moreover, we obtain existence results for weighted and anisotropic p-Laplace equation with mixed singular nonlinearities and observe that the extremals of our inequalities are associated to such singular problems.

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Weighted and anisotropic Sobolev inequality with extremal

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