On the Sub and Supersolution Method for Nonlinear Elliptic Equations with a Convective Term, in Orlicz Spaces

Giuseppina Barletta ()
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Giuseppina Barletta: Dipartimento di Ingegneria Civile, dell’Energia, dell’Ambiente e dei Materiali, Università Mediterranea di Reggio Calabria, Via Zehender, 89122 Reggio Calabria, Italy

Mathematics, 2024, vol. 12, issue 16, 1-17

Abstract: In this note we provide an overview of some existence (with sign information) and regularity results for differential equations, in which the method of sub and supersolutions plays an important role. We list some classical results and then we focus on the Dirichlet problem, for problems driven by a general differential operator, depending on ( x , u , ∇ u ) , and with a convective term f . Our framework is that of Orlicz–Sobolev spaces. We also present several examples.

Keywords: nonlinear elliptic equations; Orlicz–Sobolev spaces; gradient dependence; subsolution and supersolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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