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arXiv · 1412.6298

Very large solutions for the fractional Laplacian: towards a fractional Keller-Osserman condition

Nicola Abatangelo
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Abstract

We look for solutions of $(-Δ)^s u+f(u) = 0$ in a bounded smooth domain $Ω$, $s\in(0,1)$, with a strong singularity at the boundary. In particular, we are interested in solutions which are $L^1(Ω)$ and higher order with respect to dist$(x,\partialΩ)^{s-1}$. We provide sufficient conditions for the existence of such a solution. Roughly speaking, these functions are the real fractional counterpart of "large solutions" in the classical setting.

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Nicola Abatangelo. 2015-11-02. Very large solutions for the fractional Laplacian: towards a fractional Keller-Osserman condition. https://arxiv.org/abs/1412.6298

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