On a nonlinear Robin problem with an absorption term on the boundary and L¹ data

2023/03/30 by Della Pietra, Francesco, Oliva, Francescantonio, de León, Sergio Segura · 1 citation
#35A01 #35A02 #35J25 #35J60 #35J70 #35J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.17232

Abstract

We deal with existence and uniqueness of nonnegative solutions to \ -Δu = f(x) in Ω, (∂ u)/(∂ ν) + λ(x) u = (g(x))/(u^η) on ∂Ω, . where η≥ 0 and f,λ and g are nonnegative integrable functions. The set Ω⊂ℝ^N (N> 2) is open and bounded with smooth boundary and ν denotes its unit outward normal vector. More generally, we handle equations driven by monotone operators of p-Laplacian type jointly with nonlinear boundary conditions. We prove existence of an entropy solution and check that this solution is unique under natural assumptions. Among other features, we study the regularizing effect given to the solution by both the absorption and the nonlinear boundary term.

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• Robin problem with measure data and singular nonlinearities on the boundary

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