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.
Cite this article
Lubomira G. Softova, An Integral Estimate for the Gradient for a Class of Nonlinear Elliptic Equations in the Plane. Z. Anal. Anwend. 17 (1998), no. 1, pp. 57–66DOI 10.4171/ZAA/808