Elliptic equations with BMO coefficients in Lipschitz domains-Reference-Cited by-同舟云学术

Elliptic equations with BMO coefficients in Lipschitz domains

Published:2004-05-28 Issue:3 Volume:357 Page:1025-1046
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Byun Sun-Sig

Abstract

In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the W 1 , p ( 1 > p > ∞ ) W^{1,p}\ (1>p>\infty ) estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. These conditions for the W 1 , p W^{1,p} theory do not just weaken the requirements on the coefficients; they also lead to a more general geometric condition on the domain.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2005-357-03/S0002-9947-04-03624-4/S0002-9947-04-03624-4.pdf

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