Sobolev–Dirichlet problem for quasilinear elliptic equations in generalized Orlicz–Sobolev spaces

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
Hauptverfasser: Benyaiche, Allami, Khlifi, Ismail
Format: Artikel
Sprache:eng
Schlagworte:
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
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Zusammenfassung: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.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-020-00789-z