Abstract: We consider layer potentials for second-order divergence form elliptic operators with bounded measurable coefficients on Lipschitz domains. A ''Calderón-Zygmund" theory is developed for the boundedness of the layer potentials under the assumption that null solutions satisfy interior de Giorgi-Nash-Moser type estimates. In particular, we prove that $L^2$-estimates for layer potentials imply sharp $L^p$- and endpoint space estimates. The method of layer potentials is then used to obtain solvability of boundary value problems. This is joint work with Steve Hofmann and Marius Mitrea.
The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\infty$ coefficients
Andrew Morris (University of Birmingham)
Tue, 31/10/2017 - 15:00