Self-improving property for certain degenerate functionals with generalized Orlicz growth
Analysis of PDEs
2025-12-02 v2
Abstract
We investigate a self-improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasiminimizer has local higher integrability. In addition, we establish the existence of minimizers for the associated functional.
Cite
@article{arxiv.2511.20898,
title = {Self-improving property for certain degenerate functionals with generalized Orlicz growth},
author = {Vertti Hietanen and Mikyoung Lee},
journal= {arXiv preprint arXiv:2511.20898},
year = {2025}
}