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

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|DαAα(x,u,D1u,D2u)−Eα(x) |u|λ(pα−1) signu=f in Ω, where the coefficients Aα satisfy a strengthened degenerate coercivity condition.

Keywords

• high-order equations
• nonlinear elliptic problems
• degenerate coercivity
• convection term
• boundedness
• Hölder continuity