Weighted and anisotropic Sobolev inequality with extremal

Kaushik Bal, Prashanta Garain

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish
Pages (from-to)101-117
Number of pages17
JournalManuscripta Mathematica
Volume168
Issue number1-2
DOIs
StatePublished - 1 May 2022

ASJC Scopus subject areas

  • Mathematics (all)

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