Elliptic equations in the plane satisfying a Carleson measure condition

David Rule (Edinburgh)

Tuesday 21st October, 2008 15:00-16:00 214


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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