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

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.
Nonlinear elliptic equations
Orlicz-Sobolev spaces
Gradient dependence
Subsolution and supersolution
Truncation methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/79391
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