Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions

Damiano Greco

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arXiv · 2407.06442

Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions

Damiano Greco

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Abstract

We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for $s$-harmonic functions. Furthermore, we give sufficient conditions for distributional solutions to the fractional Poisson's equation $(-\Delta)^su=T$ on $\mathbb{R}^d$ to be of the form $$u(x)=\int_{\mathbb{R}^d}\frac{T(y)}{|x-y|^{d-2s}}dy+l,\quad l\in \mathbb{R}.$$

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Damiano Greco. 2024-07-08. Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions. https://arxiv.org/abs/2407.06442

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