Elliptic equations with BMO coefficients in Lipschitz domains

Byun, Sun-Sig

doi:10.1090/S0002-9947-04-03624-4

Elliptic equations with BMO coefficients in Lipschitz domains
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Trans. Amer. Math. Soc. 357 (2005), 1025-1046 Request permission

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 $W^{1,p}\ (1<p<\infty )$ 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 $W^{1,p}$ theory do not just weaken the requirements on the coefficients; they also lead to a more general geometric condition on the domain.

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