Bloch estimates in non-doubling generalized Orlicz spaces
Abstract
We study minimizers of non-autonomous functionals \begin{align*} \inf_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} when $\varphi$ has generalized Orlicz growth. We consider the case where the upper growth rate of $\varphi$ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function $\varphi$ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2022
- DOI:
- 10.48550/arXiv.2207.00316
- arXiv:
- arXiv:2207.00316
- Bibcode:
- 2022arXiv220700316H
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35J20 (49N60;
- 35B65;
- 31C45)
- E-Print:
- Math. Engineering 5 (2023), no. 3: 1-21