On the Neumann (p, q)-eigenvalue problem in Hölder singular domains

Prashanta Garain; Valerii Pchelintsev; Alexander Ukhlov

doi:10.1007/s00526-024-02788-4

On the Neumann (p, q)-eigenvalue problem in Hölder singular domains

Prashanta Garain, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

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

Abstract

In the article we study the Neumann (p, q)-eigenvalue problems in bounded Hölder γ-singular domains Ω_γ⊂Rⁿ. In the case 1<p<∞ and 1<q<pγ∗ we prove solvability of this eigenvalue problem and existence of the minimizer of the associated variational problem. In addition, we establish some regularity results of the eigenfunctions and some estimates of (p, q)-eigenvalues.

Original language	English
Article number	172
Journal	Calculus of Variations and Partial Differential Equations
Volume	63
Issue number	7
DOIs	https://doi.org/10.1007/s00526-024-02788-4
State	Published - 1 Sep 2024

Keywords

30C65
35A01
35J92
35P15
35P30
46E35

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s00526-024-02788-4

Cite this

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