NDLI: On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries

Content Provider	Scilit
Author	Escauriaza, L. Fabes, E. B. Verchota, G.
Copyright Year	1992
Description	We show that if $u$ is a weak solution to $\operatorname {div} (A\nabla u) = 0$ on an open set $\Omega$ containing a Lipschitz domain $D$, where $A = kI{\chi _D} + I{\chi _{\Omega /D}}(k > 0,k \ne 1)$. Then, the nontangential maximal function of the gradient of $u$ lies in ${L^2}(\partial D)$.
Related Links	https://www.ams.org/proc/1992-115-04/S0002-9939-1992-1092919-1/S0002-9939-1992-1092919-1.pdf
Ending Page	1076
Page Count	8
Starting Page	1069
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2159357
Journal	Proceedings of the American Mathematical Society
Issue Number	4
Volume Number	115
Language	English
Publisher	Duke University Press
Publisher Date	1992-08-01
Access Restriction	Open
Subject Keyword	Logic Function Regularity Theorem Weak Div Maximal Partial Nontangential
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries