Mixed Local and Nonlocal Dirichlet (p, q)-Eigenvalue Problem

P. Garain; A. Ukhlov

doi:10.1007/s10958-023-06389-y

Mixed Local and Nonlocal Dirichlet (p, q)-Eigenvalue Problem

P. Garain, A. Ukhlov

Department of Mathematics

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

6 Scopus citations

Abstract

We consider the spectral problem for the mixed local and nonlocal p-Laplace operator. We discuss the existence and regularity of eigenfunction of the associated Dirichlet (p, q)-eigenvalue problem in a bounded domain Ω ⊂ ℝ^N under the assumption that 1 < p < ∞ and 1 < q < p^∗ where p^∗ = Np/(N − p) if 1 < p < N and p^∗ = ∞ if p ⩾ N.

Original language	English
Pages (from-to)	782-792
Number of pages	11
Journal	Journal of Mathematical Sciences (United States)
Volume	270
Issue number	6
DOIs	https://doi.org/10.1007/s10958-023-06389-y
State	Published - 1 Mar 2023

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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title = "Mixed Local and Nonlocal Dirichlet (p, q)-Eigenvalue Problem",

abstract = "We consider the spectral problem for the mixed local and nonlocal p-Laplace operator. We discuss the existence and regularity of eigenfunction of the associated Dirichlet (p, q)-eigenvalue problem in a bounded domain Ω ⊂ ℝN under the assumption that 1 < p < ∞ and 1 < q < p∗ where p∗ = Np/(N − p) if 1 < p < N and p∗ = ∞ if p ⩾ N.",

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AU - Ukhlov, A.

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N2 - We consider the spectral problem for the mixed local and nonlocal p-Laplace operator. We discuss the existence and regularity of eigenfunction of the associated Dirichlet (p, q)-eigenvalue problem in a bounded domain Ω ⊂ ℝN under the assumption that 1 < p < ∞ and 1 < q < p∗ where p∗ = Np/(N − p) if 1 < p < N and p∗ = ∞ if p ⩾ N.

AB - We consider the spectral problem for the mixed local and nonlocal p-Laplace operator. We discuss the existence and regularity of eigenfunction of the associated Dirichlet (p, q)-eigenvalue problem in a bounded domain Ω ⊂ ℝN under the assumption that 1 < p < ∞ and 1 < q < p∗ where p∗ = Np/(N − p) if 1 < p < N and p∗ = ∞ if p ⩾ N.

UR - https://www.scopus.com/pages/publications/85152688979

U2 - 10.1007/s10958-023-06389-y

DO - 10.1007/s10958-023-06389-y

M3 - Article

AN - SCOPUS:85152688979

SN - 1072-3374

VL - 270

SP - 782

EP - 792

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

IS - 6

ER -

Mixed Local and Nonlocal Dirichlet (p, q)-Eigenvalue Problem

Abstract

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