Local approximation of superharmonic and superparabolic functions in nonlinear potential theory

2012/08/14 by Juha Kinnunen, Kinnunen, Juha, Teemu Lukkari +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1208.2828

arxiv created 2012/08/14 · arxiv updated 2012/08/15

Abstract

We prove that arbitrary superharmonic functions and superparabolic functions related to the p-Laplace and the p-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the corresponding Riesz measures. As an application we show that a family of uniformly bounded supersolutions to the p-parabolic equation contains a subsequence that converges to a supersolution.

Related

• Supersolutions and superharmonic functions for nonlocal operators with Orlicz growth
• Equivalence between Superharmonic functions and renormalized solutions for the equations with (p, q)-growth
• On the asymptotic behavior of p-superharmonic functions at singularities
• Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic p-Laplace equation
• Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth