On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries
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- by L. Escauriaza, E. B. Fabes and G. Verchota PDF
- Proc. Amer. Math. Soc. 115 (1992), 1069-1076 Request permission
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
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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