Equivalence between Superharmonic functions and renormalized solutions for the equations with $(p, q)$-growth
Analysis of PDEs
2025-04-17 v1
Abstract
We establish the equivalence between superharmonic functions and locally renormalized solutions for the elliptic measure data problems with -growth. By showing that locally renormalized solutions are essentially bounded below and using Wolff potential estimates, we extend the results of [T. Kilpel\"{a}inen, T. Kuusi, A. Tuhola-Kujanp\"{a}\"{a}, Superharmonic functions are locally renormalized solutions, Ann. Inst. H. Poincar\'{e} C Anal. Non Lin\'{e}aire, 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.
Keywords
Cite
@article{arxiv.2504.11719,
title = {Equivalence between Superharmonic functions and renormalized solutions for the equations with $(p, q)$-growth},
author = {Ying Li and Chao Zhang},
journal= {arXiv preprint arXiv:2504.11719},
year = {2025}
}