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 PALACHEVA, 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.File in questo prodotto:
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