Regularizing effect of absorption terms in singular problems

2018/10/31 by Oliva, Francescantonio · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.00083

Abstract

We prove existence of solutions to problems whose model is \begincases -Δ_p u + u^q = (f)/(u^γ) amp; in Ω, \newline u≥0 amp;in Ω,\newline u=0 amp;on ∂Ω, \endcases where Ω is an open bounded subset of ℝ^N (N≥2), Δ_p u is the p-laplacian operator for 1≤ p 0, γ≥ 0 and f is a nonnegative function in L^m(Ω) for some m≥1. In particular we analyze the regularizing effect produced by the absorption term in order to infer the existence of finite energy solutions in case γ≤ 1. We also study uniqueness of these solutions as well as examples which show the optimality of the results. Finally, we find local W^1,p-solutions in case γ>1.

Cited by

• Regularizing effects of absorption terms in local-nonlocal mild singular problems
• Regularizing effects for an elliptic system of singular equations

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