Towards a deterministic KPZ equation with fractional diffusion: The stationary problem

2016/09/15 by Abdellaoui, Boumediene, Peral, Ireneo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.04561

Abstract

In this work we analyze the existence of solution to the fractional quasilinear problem, \ (-Δ)^s u · amp;= · amp; |∇ u|^p+ łf · amp; in Ω, u · amp;= · amp; 0 · amp;\hbox in ℝ^N∖Ω, u · amp; · gt; · amp;0 · amp;\hbox in Ω,% .% where Ω⊂ \ren is a bounded regular domain (C² is sufficient), s∈ (\frac 12, 1), 12s.

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• Global regularity results for the fractional heat equation and application to a class of non-linear KPZ problems

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