School of Mathematical Sciences

The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\infty$ coefficients menu

The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\infty$ coefficients

Speaker: 
Andrew Morris (University of Birmingham)
Date/Time: 
Tue, 31/10/2017 - 15:00
Room: 
W316
Seminar series: 

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.