The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Elliptic problems with convection terms in Orlicz spaces / Barletta, Giuseppina; Tornatore, Elisabetta. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 1096-0813. - 495:2(2021). [10.1016/j.jmaa.2020.124779]
Elliptic problems with convection terms in Orlicz spaces
Giuseppina Barletta
;
2021-01-01
Abstract
The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.| File | Dimensione | Formato | |
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