Equivalence between Superharmonic functions and renormalized solutions for the equations with (p, q)-growth

2025/04/16 by Li, Ying, Zhang, Chao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.11719

Abstract

We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with (p, q)-growth. By showing that locally renormalized solutions are essentially bounded below and using Wolff potential estimates, we extend the results of [T. Kilpeläinen, T. Kuusi, A. Tuhola-Kujanpää, Superharmonic functions are locally renormalized solutions, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2011] to a broader class of problems. Our work provides the first equivalence result between locally renormalized solutions and superharmonic functions for the nonstandard growth equations.

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