@article{Harjulehto2023, 
author = {Petteri Harjulehto and Peter Hästö and Jonne Juusti},
title = {Bloch estimates in non-doubling generalized Orlicz spaces},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {3},
pages = {1-21},
keywords = {non-doubling, Harnack's inequality, generalized Orlicz space, Musielak–Orlicz spaces, nonstandard growth, variable exponent, double phase},
url = {https://www.sciopen.com/article/10.3934/mine.2023052},
doi = {10.3934/mine.2023052},
abstract = {We study minimizers of non-autonomous functionals                                 inf          u                          ∫          Ω                φ        (        x        ,                  |                ∇        u                  |                )                d        x            when    φ has generalized Orlicz growth. We consider the case where the upper growth rate of    φ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function    φ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.}
}