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...
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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 |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023052?viewType=HTML |
| _version_ | 1797743381736062976 |
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| author | Petteri Harjulehto Peter Hästö Jonne Juusti |
| author_facet | Petteri Harjulehto Peter Hästö Jonne Juusti |
| author_sort | Petteri Harjulehto |
| collection | DOAJ |
| description | <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> |
| first_indexed | 2024-03-12T14:54:41Z |
| format | Article |
| id | doaj.art-7988ba7cbfdf4429b00a8fe5fa19ab99 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-12T14:54:41Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-7988ba7cbfdf4429b00a8fe5fa19ab992023-08-15T01:37:38ZengAIMS PressMathematics in Engineering2640-35012023-08-015312110.3934/mine.2023052Bloch estimates in non-doubling generalized Orlicz spacesPetteri Harjulehto0Peter Hästö1Jonne Juusti 21. Department of Mathematics and Statistics, FI-00014 University of Helsinki, Finland2. Department of Mathematics and Statistics, FI-20014 University of Turku, Finland2. Department of Mathematics and Statistics, FI-20014 University of Turku, Finland<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>https://www.aimspress.com/article/doi/10.3934/mine.2023052?viewType=HTMLnon-doublingharnack's inequalitygeneralized orlicz spacemusielak–orlicz spacesnonstandard growthvariable exponentdouble phase |
| spellingShingle | Petteri Harjulehto Peter Hästö Jonne Juusti Bloch estimates in non-doubling generalized Orlicz spaces Mathematics in Engineering non-doubling harnack's inequality generalized orlicz space musielak–orlicz spaces nonstandard growth variable exponent double phase |
| title | Bloch estimates in non-doubling generalized Orlicz spaces |
| title_full | Bloch estimates in non-doubling generalized Orlicz spaces |
| title_fullStr | Bloch estimates in non-doubling generalized Orlicz spaces |
| title_full_unstemmed | Bloch estimates in non-doubling generalized Orlicz spaces |
| title_short | Bloch estimates in non-doubling generalized Orlicz spaces |
| title_sort | bloch estimates in non doubling generalized orlicz spaces |
| topic | non-doubling harnack's inequality generalized orlicz space musielak–orlicz spaces nonstandard growth variable exponent double phase |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023052?viewType=HTML |
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