Elliptic equations in the plane satisfying a Carleson measure condition

20 November 2008
12:00
Abstract
We study the Neumann and regularity boundary value problems for a divergence form elliptic equation in the plane. We assume the gradient of the coefficient matrix satisfies a Carleson measure condition and consider data in L^p, 1 < p \leq 2. We prove that if the norm of the Carleson measure is sufficiently small, we can solve both the Neumann and regularity problems with data in L^p. This is related to earlier work on the Dirichlet problem by other authors.
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