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A Priori Estimate for the Discontinuous Oblique Derivative Problem for Elliptic Systems

✍ Scribed by Heinrich Begehr; Guo-Chun Wen

Publisher: John Wiley and Sons
Year: 1989
Tongue: English
Weight: 950 KB
Volume: 142
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19891420122

No coin nor oath required. For personal study only.

✦ Synopsis

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, 231 wa.s proved, based on some a priori estimate from [ZO]. This estjmate, however, i Y 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 [ll], 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 [!I].

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