An a priori estimate is established for the gradient of the solution to Dirichlet's problem for a class of nonlinear differential equations on a convex domain in the plane. The nonlinear operator is assumed to be elliptic in the sense of Campanato. By virtue of the Leray-Schauder fixed point theorem an existence result for the problem under consideration is derived.

An integral estimate for the gradient for a class of nonlinear elliptic equations in the plane,

SOFTOVA PALAGACHEVA, Lyoubomira
1998

Abstract

An a priori estimate is established for the gradient of the solution to Dirichlet's problem for a class of nonlinear differential equations on a convex domain in the plane. The nonlinear operator is assumed to be elliptic in the sense of Campanato. By virtue of the Leray-Schauder fixed point theorem an existence result for the problem under consideration is derived.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/220955
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