Existence results for nonlocal problems governed by the regional fractional Laplacian

Mouhamed Moustapha Fall; Remi Yvant Temgoua

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arXiv · 2112.06272

Existence results for nonlocal problems governed by the regional fractional Laplacian

Mouhamed Moustapha Fall·Remi Yvant Temgoua

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Abstract

The aim of the present paper is to study existence results of minimizers of the critical fractional Sobolev constant on bounded domains. Under some values of the fractional parameter we show that the best constant is achieved. If moreover the underlying domain is a ball, we obtain positive radial minimizers for all possible values of the fractional parameter in higher dimension, while we impose a positive mass condition in low dimension.

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Mouhamed Moustapha Fall, Remi Yvant Temgoua. 2021-12-12. Existence results for nonlocal problems governed by the regional fractional Laplacian. https://arxiv.org/abs/2112.06272

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