Regularity of solutions in semilinear elliptic theory

2016/01/20 by Emanuel Indrei, Indrei, Emanuel, Andreas Minne +3
Computer Science · Mathematics · #35J61 #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.1601.05219

openalex publication_date 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the semilinear Poisson equation Δu = f(x, u) \hskip .2 in in \hskip .2 in B₁. Our main results provide conditions on f which ensure that weak solutions of this equation belong to C^1,1(B_1/2). In some configurations, the conditions are sharp.

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