Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries


Authors: L. Escauriaza, E. B. Fabes and G. Verchota
Journal: Proc. Amer. Math. Soc. 115 (1992), 1069-1076
MSC: Primary 35B65; Secondary 35J15
DOI: https://doi.org/10.1090/S0002-9939-1992-1092919-1
MathSciNet review: 1092919
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: 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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35B65, 35J15

Retrieve articles in all journals with MSC: 35B65, 35J15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1092919-1
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society