Mixed anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problem

Prashanta Garain; Alexander Ukhlov

Mixed anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problem

Prashanta Garain
, Alexander Ukhlov

Department of Mathematics

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

1 Scopus citations

Abstract

In this article, we consider an anisotropic and a combination of anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problems. We establish existence and regularity of eigenfunctions in a bounded domain Ω ⊂ R^N under the assumption that 1 < p < ∞ and 1 < q < p^∗ where (Formula presented) < N and p^∗ = ∞ if p ≥ N.

Original language	English
Pages (from-to)	217-232
Number of pages	16
Journal	Rivista di Matematica della Universita di Parma
Volume	14
Issue number	1
State	Published - 1 Jan 2023

Keywords

Anisotropic p-Laplace operator
Dirichlet eigenvalue problem
Mixed local and nonlocal p-Laplacian
existence
regularity

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Mixed anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problem",

abstract = "In this article, we consider an anisotropic and a combination of anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problems. We establish existence and regularity of eigenfunctions in a bounded domain Ω ⊂ RN under the assumption that 1 < p < ∞ and 1 < q < p∗ where (Formula presented) < N and p∗ = ∞ if p ≥ N.",

keywords = "Anisotropic p-Laplace operator, Dirichlet eigenvalue problem, Mixed local and nonlocal p-Laplacian, existence, regularity",

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T1 - Mixed anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problem

AU - Garain, Prashanta

AU - Ukhlov, Alexander

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N2 - In this article, we consider an anisotropic and a combination of anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problems. We establish existence and regularity of eigenfunctions in a bounded domain Ω ⊂ RN under the assumption that 1 < p < ∞ and 1 < q < p∗ where (Formula presented) < N and p∗ = ∞ if p ≥ N.

AB - In this article, we consider an anisotropic and a combination of anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problems. We establish existence and regularity of eigenfunctions in a bounded domain Ω ⊂ RN under the assumption that 1 < p < ∞ and 1 < q < p∗ where (Formula presented) < N and p∗ = ∞ if p ≥ N.

KW - Anisotropic p-Laplace operator

KW - Dirichlet eigenvalue problem

KW - Mixed local and nonlocal p-Laplacian

KW - existence

KW - regularity

UR - https://www.scopus.com/pages/publications/85174502975

M3 - Article

AN - SCOPUS:85174502975

SN - 0035-6298

VL - 14

SP - 217

EP - 232

JO - Rivista di Matematica della Universita di Parma

JF - Rivista di Matematica della Universita di Parma

IS - 1

ER -

Mixed anisotropic and nonlocal Dirichlet (p, q)-eigenvalue problem

Abstract

Keywords

ASJC Scopus subject areas

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