WEIGHTED ANISOTROPIC SOBOLEV INEQUALITY WITH EXTREMAL AND ASSOCIATED SINGULAR PROBLEMS

Kaushik Bal; Prashanta Garain

doi:10.57262/die036-0102-59

WEIGHTED ANISOTROPIC SOBOLEV INEQUALITY WITH EXTREMAL AND ASSOCIATED SINGULAR PROBLEMS

Kaushik Bal, Prashanta Garain

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

7 Scopus citations

Abstract

We consider singular problems associated with the weighted anisotropic p-Laplace operator Hp, wu = div(w(x)(H(∇u))^p-1∇H(∇u)), where H is a Finsler-Minkowski norm and the weight w belongs to a class of p-admissible weights, which may vanish or blow up near the origin. We discuss existence and regularity properties of weak solutions for the mixed and exponential singular nonlinearities. In particular, the existence result for the purely singular problem leads us to the validity of a weighted anisotropic Sobolev inequality with an extremal.

Original language	English
Pages (from-to)	59-92
Number of pages	34
Journal	Differential and Integral Equations
Volume	36
Issue number	1-2
DOIs	https://doi.org/10.57262/die036-0102-59
State	Published - 1 Jan 2023
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "We consider singular problems associated with the weighted anisotropic p-Laplace operator Hp, wu = div(w(x)(H(∇u))p-1∇H(∇u)), where H is a Finsler-Minkowski norm and the weight w belongs to a class of p-admissible weights, which may vanish or blow up near the origin. We discuss existence and regularity properties of weak solutions for the mixed and exponential singular nonlinearities. In particular, the existence result for the purely singular problem leads us to the validity of a weighted anisotropic Sobolev inequality with an extremal.",

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AB - We consider singular problems associated with the weighted anisotropic p-Laplace operator Hp, wu = div(w(x)(H(∇u))p-1∇H(∇u)), where H is a Finsler-Minkowski norm and the weight w belongs to a class of p-admissible weights, which may vanish or blow up near the origin. We discuss existence and regularity properties of weak solutions for the mixed and exponential singular nonlinearities. In particular, the existence result for the purely singular problem leads us to the validity of a weighted anisotropic Sobolev inequality with an extremal.

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WEIGHTED ANISOTROPIC SOBOLEV INEQUALITY WITH EXTREMAL AND ASSOCIATED SINGULAR PROBLEMS

Abstract

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