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RESEARCH PRODUCT

Elliptic problems with convection terms in Orlicz spaces

Elisabetta TornatoreGiuseppina Barletta

subject

Dirichlet problemGradient dependenceClass (set theory)Truncation methodsTruncationApplied Mathematics010102 general mathematicsZero (complex analysis)Orlicz-Sobolev spacesNonlinear elliptic equationsTerm (logic)01 natural sciences010101 applied mathematicsNonlinear systemOperator (computer programming)Subsolution and supersolutionSettore MAT/05 - Analisi MatematicaApplied mathematics0101 mathematicsAnalysisMathematicsVariable (mathematics)

description

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.

yearjournalcountryeditionlanguage
2021-03-15Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2020.124779