Bloch estimates in non-doubling generalized Orlicz spaces
Analysis of PDEs
2022-09-27 v2
Abstract
We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} when has generalized Orlicz growth. We consider the case where the upper growth rate of is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.
Cite
@article{arxiv.2207.00316,
title = {Bloch estimates in non-doubling generalized Orlicz spaces},
author = {Petteri Harjulehto and Peter Hästö and Jonne Juusti},
journal= {arXiv preprint arXiv:2207.00316},
year = {2022}
}