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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)
Record Type:
Journal Article
Title:
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)
Main Title:
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).
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 .