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A Remark on the Sobolev Regularity of Classical Solutions of Strongly Elliptic Equations

โœ Scribed by Albert Milani

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
666 KB
Volume
190
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

We prove that C2*" (a) solutions of problem (1.2) below are in H"+2(i2) for all m E IN, if f and the coefficients are in Hm(52) n Cola (a) . Previously, this result was explicitly known only if m > n/2 (or if m = 0). A similar result holds for the quasi-linear equation (1.11) below. of IR* ; in the next sections, we recall some well known results on Classical and Sobolev 1991 Mathematics Subject Classification.

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## Abstract Let u be a vector field on a bounded Lipschitz domain in โ„^3^, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space __H__^1/2^ on the domain