Towards a deterministic KPZ equation with fractional diffusion: the stationary problem*The authors were partially supported by Ministerio de Economia y Competitividad under grants MTM2013-40846-P and MTM2016-80474-P (Spain). (20th February 2018) - Abdellaoui, Boumediene; Peral, Ireneo
Abstract: In this work, we investigate by analysis the possibility of a solution to the fractional quasilinear problem: where is a bounded regular domain ( is sufficient), , 1  <   q and f is a measurable non-negative function with suitable hypotheses. The analysis is done separately in three cases: subcritical, 1  <   q   <  2 s ; critical, q   =  2 s ; and supercritical, q   >  2 s .