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arXiv · 2303.03054

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

Prashanta Garain·Alexander Ukhlov
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Abstract

In this article, 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 $\Omega\subset\mathbb{R}^N$ under the assumption that $1<p<\infty$ and $1<q<p^{*}$ where $p^{*}=\frac{N p}{N-p}$ if $1<p<N$ and $p^{*}=\infty$ if $p\geq N$.

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Prashanta Garain, Alexander Ukhlov. 2023-03-06. Mixed local and nonlocal Dirichlet $(p,q)$-eigenvalue problem. https://arxiv.org/abs/2303.03054

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