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

2014/12/19 by Abatangelo, Nicola · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.6298

Abstract

We look for solutions of (-Δ)^s u+f(u) = 0 in a bounded smooth domain Ω, s∈(0,1), with a strong singularity at the boundary. In particular, we are interested in solutions which are L¹(Ω) and higher order with respect to dist(x,∂Ω)^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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