Isocapacitary constants for the $p$-Laplacian on compact manifolds

Lili Wang; Tao Wang

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arXiv · 2512.24725

Isocapacitary constants for the $p$-Laplacian on compact manifolds

Lili Wang·Tao Wang

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Abstract

In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,\alpha)$-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the $p$-Laplacian when $\alpha= 1$.

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BibTeX RIS

Lili Wang, Tao Wang. 2025-12-31. Isocapacitary constants for the $p$-Laplacian on compact manifolds. https://arxiv.org/abs/2512.24725

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