Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces
In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev–Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz–Sobolev spaces on domains, not necessarily bounded, of R N . Our approach is based on solving the obstacle problem and usi...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2021-07, Vol.25 (3), p.819-841 |
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| container_title | Positivity : an international journal devoted to the theory and applications of positivity in analysis |
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| creator | Benyaiche, Allami Khlifi, Ismail |
| description | In this paper, we prove existence, uniqueness, and local regularity of the solution to the Sobolev–Dirichlet problem for quasilinear elliptic equations in the generalized Orlicz–Sobolev spaces on domains, not necessarily bounded, of
R
N
. Our approach is based on solving the obstacle problem and using the Harnack inequality. |
| doi_str_mv | 10.1007/s11117-020-00789-z |
| format | Article |
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R
N
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| identifier | ISSN: 1385-1292 |
| ispartof | Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2021-07, Vol.25 (3), p.819-841 |
| issn | 1385-1292 1572-9281 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals; Business Source Complete |
| subjects | Calculus of Variations and Optimal Control Optimization Dirichlet problem Econometrics Elliptic functions Fourier Analysis Inequality Mathematical analysis Mathematics Mathematics and Statistics Operator Theory Partial differential equations Potential Theory Sobolev space |
| title | Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces |
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