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Hardy inequalities and nonlocal capacity

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arxiv 2410.10001 v1 pith:DUDVJVTI submitted 2024-10-13 math.AP math.FA

Tomasz Grzywny , Julia Lenczewska This is my paper · ORCID
classification math.APmath.FA
keywords nonlocalcapacitiesinequalitiessobolevspacesarticleballcapacity
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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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  1. The Dirichlet Problem For the Logarithmic p-Laplacian

    math.AP 2024-11 conditional novelty 7.0 of 10

    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 Ha...

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