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Zeitschrift für Analysis und ihre Anwendungen


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Volume 17, Issue 1, 1998, pp. 57–66
DOI: 10.4171/ZAA/808

Published online: 1998-03-31

An Integral Estimate for the Gradient for a Class of Nonlinear Elliptic Equations in the Plane

Lubomira G. Softova[1]

(1) Seconda Università degli Studi di Napoli, Aversa, Italy

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.

Keywords: Nonlinear elliptic equations, a priori estimates, Aleksandrov-Pucci maximum principle

Softova Lubomira: An Integral Estimate for the Gradient for a Class of Nonlinear Elliptic Equations in the Plane. Z. Anal. Anwend. 17 (1998), 57-66. doi: 10.4171/ZAA/808