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Optimal conditions for a priori estimates for semilinear elliptic systems with two components

โœ Scribed by Li Yuxiang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
889 KB
Volume
72
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

In this paper, we present a new bootstrap procedure for elliptic systems with two unknown functions. When combined with the L p -L q -estimates, it yields the optimal L โˆž -regularity conditions for the three well-known types of weak solutions: H 1 0 -solutions, L 1 -solutions and L 1 ฮด -solutions. Thanks to the linear theory in L p ฮด (โ„ฆ), it also yields the optimal conditions for a priori estimates for L 1 ฮด -solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.

๐Ÿ“œ SIMILAR VOLUMES

A Priori Estimate for the Discontinuous
A Priori Estimate for the Discontinuous Oblique Derivative Problem for Elliptic Systems
โœ Heinrich Begehr; Guo-Chun Wen ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 950 KB

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