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A Priori Estimate for the Discontinuous Oblique Derivative Problem for Elliptic Systems
Author(s) -
Begehr Heinrich,
Wen GuoChun
Publication year - 1989
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19891420122
Subject(s) - mathematics , a priori and a posteriori , oblique case , uniqueness , nonlinear system , a priori estimate , derivative (finance) , reductio ad absurdum , mathematical analysis , constant (computer programming) , interpretation (philosophy) , computer science , physics , philosophy , linguistics , epistemology , quantum mechanics , financial economics , economics , programming language
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].