The regularity and Neumann problem for non-symmetric elliptic operators

Kenig, Carlos; Rule, David

doi:10.1090/S0002-9947-08-04610-2

The regularity and Neumann problem for non-symmetric elliptic operators
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by Carlos E. Kenig and David J. Rule PDF

Trans. Amer. Math. Soc. 361 (2009), 125-160 Request permission

Abstract:

We establish optimal $L^p$ bounds for the non-tangential maximal function of the gradient of the solution to a second-order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the vertical variable, on the domain above a Lipschitz graph in the plane, in terms of the $L^p$-norm at the boundary of the tangential derivative of the Dirichlet data, or of the Neumann data.

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