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We establish two commutator estimates for the Dirichlet-to-Neumann map associated with a second-order elliptic system in divergence form in Lipschitz domains.
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G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains , J. Funct. Anal. 59
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B. Dahlberg, C. Kenig, and G. Verchota, The Dirichlet problem for the biharmonic equation in a Lipschitz domain , Ann. Inst. Fourier (Grenoble) 36
1986
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B. Dahlberg, C. Kenig, J. Pipher, and G. Verchota, Area integral estimates for higher order elliptic equations and systems , Ann. Inst. Fourier (Grenoble) 47
1997
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M. Mitrea and M. Taylor, Potential theory on Lipschitz domains in Riemannian manifolds: Hölder continuous metric tensors , Comm. PDEs 25
2000
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C. Kenig, F. Lin, and Z. Shen, Periodic homogenization of Green and Neumann functions , Comm. Pure Appl. Math. (to appear)
Cited in the paper.
L. Grafakos, Classical and Modern Fourier Analysis , Pearson Education, Inc., Upper Saddle River, New Jersey 07458, 2004
2004
Later among the works it cites.
S. Hofmann, Dahlberg’s bilinear estimate for solutions of divergence form complex elliptic equations , Proc. Amer. Math. Soc. 136
2008
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C. Kenig and Z. Shen, Layer potential methods for elliptic homogenization problems , Comm. Pure Appl. Math. 64
2011
Later among the works it cites.
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