Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations

2012/01/27 by Matteo Bonforte, Bonforte, Matteo, Gabriele Grillo +3
Computer Science · Mathematics · #35B45 #35B65 #35K55 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35B45 #msc:35B65 #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.1201.5801

2 figures

arxiv created 2012/01/27 · openalex publication_date 2012/01/27 · arxiv updated 2012/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form -Δu= c u^p, with 0

Citations

• A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations
• Semilinear elliptic equations and supercritical growth
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

Related

• On the regularity theory for mixed local and nonlocal quasilinear elliptic equations
• On the smoothness of weak solutions to subcritical semilinear elliptic\n equations in any dimension
• Uniform a priori bounds for Slightly Subcritical Elliptic Problems
• Regularity and Symmetry for Semilinear Elliptic Equations in Bounded Domains
• Local boundedness for weak solutions to some quasilinear elliptic systems