WEIGHTED ANISOTROPIC SOBOLEV INEQUALITY WITH EXTREMAL AND ASSOCIATED SINGULAR PROBLEMS

Kaushik Bal, Prashanta Garain

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)59-92
Number of pages34
JournalDifferential and Integral Equations
Volume36
Issue number1-2
DOIs
StatePublished - 1 Jan 2023
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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