On the local behavior of local weak solutions to some singular anisotropic elliptic equations
We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\partial }_{i}({A}_{i}\left(x,u,\nabla u))=0,\...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-09-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2022-0275 |
| _version_ | 1811205267520487424 |
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| author | Ciani Simone Skrypnik Igor I. Vespri Vincenzo |
| author_facet | Ciani Simone Skrypnik Igor I. Vespri Vincenzo |
| author_sort | Ciani Simone |
| collection | DOAJ |
| description | We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\partial }_{i}({A}_{i}\left(x,u,\nabla u))=0,\hspace{1.0em}x\in \Omega \subset \hspace{-0.3em}\subset \hspace{0.33em}{{\mathbb{R}}}^{N}\hspace{1.0em}\hspace{0.1em}\text{for}\hspace{0.1em}\hspace{0.33em}1\le s\le \left(N-1), where each operator Ai{A}_{i} behaves directionally as the singular pp-Laplacian, 1<p<21\lt p\lt 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Hölder continuity and some integral and pointwise Harnack inequalities. |
| first_indexed | 2024-04-12T03:27:55Z |
| format | Article |
| id | doaj.art-0300f9efc3004defa669c72ad0e55a5b |
| institution | Directory Open Access Journal |
| issn | 2191-950X |
| language | English |
| last_indexed | 2024-04-12T03:27:55Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-0300f9efc3004defa669c72ad0e55a5b2022-12-22T03:49:37ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2022-09-0112123726510.1515/anona-2022-0275On the local behavior of local weak solutions to some singular anisotropic elliptic equationsCiani Simone0Skrypnik Igor I.1Vespri Vincenzo2Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, GermanyInstitute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Gen. Batiouk Str. 19, 84116 Sloviansk, UkraineDipartimento di Matematica e Informatica “Ulisse Dini” Viale G. Morgagni, Università degli Studi di Firenze, 67/a, 50134 Firenze, ItalyWe study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\partial }_{i}({A}_{i}\left(x,u,\nabla u))=0,\hspace{1.0em}x\in \Omega \subset \hspace{-0.3em}\subset \hspace{0.33em}{{\mathbb{R}}}^{N}\hspace{1.0em}\hspace{0.1em}\text{for}\hspace{0.1em}\hspace{0.33em}1\le s\le \left(N-1), where each operator Ai{A}_{i} behaves directionally as the singular pp-Laplacian, 1<p<21\lt p\lt 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Hölder continuity and some integral and pointwise Harnack inequalities.https://doi.org/10.1515/anona-2022-0275anisotropic p-laplaciansingular parabolic equationshölder continuityintrinsic scalingexpansion of positivityintrinsic harnack inequality35j7535k9235b65 |
| spellingShingle | Ciani Simone Skrypnik Igor I. Vespri Vincenzo On the local behavior of local weak solutions to some singular anisotropic elliptic equations Advances in Nonlinear Analysis anisotropic p-laplacian singular parabolic equations hölder continuity intrinsic scaling expansion of positivity intrinsic harnack inequality 35j75 35k92 35b65 |
| title | On the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| title_full | On the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| title_fullStr | On the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| title_full_unstemmed | On the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| title_short | On the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| title_sort | on the local behavior of local weak solutions to some singular anisotropic elliptic equations |
| topic | anisotropic p-laplacian singular parabolic equations hölder continuity intrinsic scaling expansion of positivity intrinsic harnack inequality 35j75 35k92 35b65 |
| url | https://doi.org/10.1515/anona-2022-0275 |
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