Bloch estimates in non-doubling generalized Orlicz spaces
<p>We study minimizers of non-autonomous functionals</p> <p class="disp_formula">$ \begin{align*} \inf\limits_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} $</p> <p>when $ \varphi $ has generalized Orlicz growth. We consider the case where the u...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-08-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023052?viewType=HTML |
| Summary: | <p>We study minimizers of non-autonomous functionals</p>
<p class="disp_formula">$ \begin{align*} \inf\limits_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} $</p>
<p>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.</p> |
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| ISSN: | 2640-3501 |