On Indirect Approach to the Solvability of Quasi-Linear Dirichlet Elliptic Boundary Value Problem with BMO-Anisotropic p-Laplacian
We study here Dirichlet boundary value problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principle part and L^1-control in coefficient of the low-order term. As characteristic feature of such problem is a specification of the matrix of anisotropy A=A^{sym}+A^{s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Oles Honchar Dnipro National University
2018-12-01
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| Series: | Journal of Optimization, Differential Equations and Their Applications |
| Subjects: | |
| Online Access: | https://model-dnu.dp.ua/index.php/SM/article/view/129 |
| Summary: | We study here Dirichlet boundary value problem for a quasi-linear elliptic equation with anisotropic p-Laplace operator in its principle part and L^1-control in coefficient of the low-order term. As characteristic feature of such problem is a specification of the matrix of anisotropy A=A^{sym}+A^{skew} in BMO-space. Since we cannot expect to have a solution of the state equation in the classical Sobolev space W^{1,p}_0(\Omega), we specify a suitable functional class in which we look for solutions and prove existence of weak solutions in the sense of Minty using a non standard approximation procedure and compactness arguments in variable spaces. |
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| ISSN: | 2617-0108 2663-6824 |