The paper introduces the logarithmic p-Laplacian and proves its first eigenvalue is the s to 0 derivative of the fractional p-Laplacian eigenvalue, with eigenfunction convergence, maximum principles, and a boundary Hardy inequality.
Hardy inequalities and nonlocal capacity
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abstract
In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove Hardy-type inequalities to obtain Sobolev embeddings and use them to estimate the nonlocal capacities of a ball.
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2024 1verdicts
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The Dirichlet Problem For the Logarithmic p-Laplacian
The paper introduces the logarithmic p-Laplacian and proves its first eigenvalue is the s to 0 derivative of the fractional p-Laplacian eigenvalue, with eigenfunction convergence, maximum principles, and a boundary Hardy inequality.