Weak solutions for anisotropic nonlinear elliptic equations with variable exponents
We study the anisotropic boundary-value problem $$displaylines{ -sum^{N}_{i=1}frac{partial}{partial x_{i}}a_{i}(x,frac{partial}{partial x_{i}}u)=f quad hbox{in } Omega, cr u=0 quadhbox{on }partial Omega, }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^{N}$ $(Ngeq 3)$. We obtain th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2009-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/144/abstr.html |
| _version_ | 1828310016675807232 |
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| author | Sado Traore Stanislas Ouaro Blaise Kone |
| author_facet | Sado Traore Stanislas Ouaro Blaise Kone |
| author_sort | Sado Traore |
| collection | DOAJ |
| description | We study the anisotropic boundary-value problem $$displaylines{ -sum^{N}_{i=1}frac{partial}{partial x_{i}}a_{i}(x,frac{partial}{partial x_{i}}u)=f quad hbox{in } Omega, cr u=0 quadhbox{on }partial Omega, }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^{N}$ $(Ngeq 3)$. We obtain the existence and uniqueness of a weak energy solution for $fin L^{infty}(Omega)$, and the existence of weak energy solution for general data $f$ dependent on $u$. |
| first_indexed | 2024-04-13T15:37:48Z |
| format | Article |
| id | doaj.art-99315f62e91b46d69a1f122fe9d9ce5f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T15:37:48Z |
| publishDate | 2009-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-99315f62e91b46d69a1f122fe9d9ce5f2022-12-22T02:41:14ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-11-012009144,111Weak solutions for anisotropic nonlinear elliptic equations with variable exponentsSado TraoreStanislas OuaroBlaise KoneWe study the anisotropic boundary-value problem $$displaylines{ -sum^{N}_{i=1}frac{partial}{partial x_{i}}a_{i}(x,frac{partial}{partial x_{i}}u)=f quad hbox{in } Omega, cr u=0 quadhbox{on }partial Omega, }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^{N}$ $(Ngeq 3)$. We obtain the existence and uniqueness of a weak energy solution for $fin L^{infty}(Omega)$, and the existence of weak energy solution for general data $f$ dependent on $u$.http://ejde.math.txstate.edu/Volumes/2009/144/abstr.htmlAnisotropic Sobolev spacesweak energy solutionvariable exponentselectrorheological fluids |
| spellingShingle | Sado Traore Stanislas Ouaro Blaise Kone Weak solutions for anisotropic nonlinear elliptic equations with variable exponents Electronic Journal of Differential Equations Anisotropic Sobolev spaces weak energy solution variable exponents electrorheological fluids |
| title | Weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| title_full | Weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| title_fullStr | Weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| title_full_unstemmed | Weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| title_short | Weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| title_sort | weak solutions for anisotropic nonlinear elliptic equations with variable exponents |
| topic | Anisotropic Sobolev spaces weak energy solution variable exponents electrorheological fluids |
| url | http://ejde.math.txstate.edu/Volumes/2009/144/abstr.html |
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