Local boundedness of weak solutions to elliptic equations with p,q−growth
This article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the <italic>local boundedness</italic> of weak solutions to a class of nonlinea...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023065?viewType=HTML |
| _version_ | 1827792813846167552 |
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| author | Giovanni Cupini Paolo Marcellini Elvira Mascolo |
| author_facet | Giovanni Cupini Paolo Marcellini Elvira Mascolo |
| author_sort | Giovanni Cupini |
| collection | DOAJ |
| description | This article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the <italic>local boundedness</italic> of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type considered below in (1.1), under $ p, q- $growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on $ u $, other than on its gradient $ Du $ and on the $ x $ variable. |
| first_indexed | 2024-03-11T18:08:35Z |
| format | Article |
| id | doaj.art-bd3c0f5bbe8e4000899684e77628a8d0 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-11T18:08:35Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-bd3c0f5bbe8e4000899684e77628a8d02023-10-17T01:13:01ZengAIMS PressMathematics in Engineering2640-35012023-09-015312810.3934/mine.2023065Local boundedness of weak solutions to elliptic equations with p,q−growthGiovanni Cupini 0Paolo Marcellini 1Elvira Mascolo21. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 - Bologna, Italy2. Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 - Firenze, Italy2. Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 - Firenze, ItalyThis article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the <italic>local boundedness</italic> of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type considered below in (1.1), under $ p, q- $growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on $ u $, other than on its gradient $ Du $ and on the $ x $ variable.https://www.aimspress.com/article/doi/10.3934/mine.2023065?viewType=HTMLregularitylocal boundednessweak solutionselliptic equations$ p， q- $growth |
| spellingShingle | Giovanni Cupini Paolo Marcellini Elvira Mascolo Local boundedness of weak solutions to elliptic equations with p,q−growth Mathematics in Engineering regularity local boundedness weak solutions elliptic equations $ p， q- $growth |
| title | Local boundedness of weak solutions to elliptic equations with p,q−growth |
| title_full | Local boundedness of weak solutions to elliptic equations with p,q−growth |
| title_fullStr | Local boundedness of weak solutions to elliptic equations with p,q−growth |
| title_full_unstemmed | Local boundedness of weak solutions to elliptic equations with p,q−growth |
| title_short | Local boundedness of weak solutions to elliptic equations with p,q−growth |
| title_sort | local boundedness of weak solutions to elliptic equations with p q growth |
| topic | regularity local boundedness weak solutions elliptic equations $ p， q- $growth |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023065?viewType=HTML |
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