On the smoothness of weak solutions to subcritical semilinear elliptic\n equations in any dimension

2021/04/20 by Rosa Pardo San Gil, Pardo, Rosa
Computer Science · Mathematics · #35B09 #35B33 #35B45 #35B65 #35J60 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.10104

openalex publication_date 2021/04/20 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/04

Abstract

Let us consider a semilinear boundary value problem - \Δ u= f(x,u), in\n\Ω, with Dirichlet boundary conditions, where \Ω \⊂\n\ℝ^N , N> 2, is a bounded smooth domain. We provide sufficient\nconditions guarantying that semi-stable weak positive solutions to subcritical\nsemilinear elliptic equations are smooth in any dimension, and as a\nconsequence, classical solutions. By a subcritical nonlinearity we mean\nf(x,s)/s^\(N+2)/(N-2) \→ 0 as s\→\∞, including non-power\nnonlinearities, and enlarging the class of subcritical nonlinearities, which is\nusually reserved for power like nonlinearities.\n

Citations

• Quasilinear Dirichlet problems driven by positive sources

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