Analysis and Probability Theory Seminar

We prove solvability results for these three types of boundary value problems for second order divergence form elliptic systems on manifolds with Lipschitz boundaries. Coefficients are bounded, accretive and measurable, satisfying a Carleson condition near the boundary, and solvability results are obtained in weighted L_2 norms of boundary data. We show how hard estimates from harmonic analysis are combined with soft estimates from Fredholm theory to prove solvability.

This is joint work with Pascal Auscher and Andrew Morris.