| Abstract: | Recently 6] an existence as well as a uniqueness theorem for the discontinuous oblique derivative problem for nonlinear elliptic system of first order in the plane, see 12, 19, 23] was proved, based on some a priori estimate from 20]. This estimate, however, is deduced by reductio ad absurdum. Therefore the constants in this estimate are unknown so that the estimate cannot be used for numerical procedures, e.g. for approximating the solution of a nonlinear problem by solutions of related linear problems, see 24, 3, 4]. In this paper a direct proof of an a priori estimate is given using some variations of results from 14], see also 11], where the constants can explicitely be estimated. For related a priori estimates see 1 – 5, 8, 16, 17, 20, 21, 24 – 26]. A basic reference for the oblique derivative problem is 9]. |
