Abstract
Our aim is to study the oblique derivative problem for a class of nonlinear differential operators in the plane with quadratic growth. We assume the discontinuous operators to satisfy Carathéodory's condition and a suitable ellipticity condition. Under some geometrical conditions we prove strong solvability of the problem under consideration. The main tool in the proof is Leray-Schauder fixed point theorem, that reduces the solvability of the problem to the establishment of a priori estimate, by means of a step by step procedure.
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