Existence of Bounded Solutions for a Class of Degenerate Fourth-Order Elliptic Equations with Convection Terms

Salvatore D’Asero ()
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Salvatore D’Asero: Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Mathematics, 2024, vol. 13, issue 1, 1-19

Abstract: This paper deals with the existence of bounded and locally Hölder continuous weak solutions of the following nonlinear fourth-order Dirichlet problem: ∑ | α | = 1 , 2 ( − 1 ) | α | D α A α ( x , u , D 1 u , D 2 u ) − E α ( x ) | u | λ ( p α − 1 ) sign u = f in Ω , where the coefficients A α satisfy a strengthened degenerate coercivity condition.

Keywords: high-order equations; nonlinear elliptic problems; degenerate coercivity; convection term; boundedness; Hölder continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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