Fractional KPZ equations with critical growth in the gradient respect to Hardy potential

2020/02/06 by Abdellaoui, Boumediene, Peral, Ireneo, Primo, Ana +1
#35J62 #35J75 #35R09 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.02201

Abstract

In this work we study the existence of positive solution to the fractional quasilinear problem, \ (-Δ)^s u · amp;= · amp;λ\dfracu|x|^2s+ |∇ u|^p+ μf · amp;\inn Ω,
u · amp; · gt; · amp;0 · amp; \innΩ,
u · amp;= · amp;0 · amp; \inn(ℝ^N∖Ω),. where Ω is a C^1,1 bounded domain in ℝ^N, N> 2s, μ>0, (1)/(2)0, there exists a critical exponent p₊(λ, s) such that for p> p₊(λ,s) there is no positive solution. Moreover, p₊(λ,s) is optimal in the sense that, if p

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