### Abstract:

We consider the layer potentials associated with operators $L=-\mathrm{div}A \nabla$ acting in the upper half-space

$\mathbb{R}^{n+1}_+$, $n\geq 2$, where the coefficient matrix $A$ is complex, elliptic, bounded, measurable, and $t$-independent.  A Calder\'{o}n--Zygmund" theory is developed for the boundedness of the layer potentials under the assumption that solutions of the equation $Lu=0$ satisfy interior De Giorgi--Nash--Moser type estimates. In particular, we prove that $L^2$ estimates for the 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.

Speaker

Andrew Morris

Research Area
Affiliation

University of Oxford

Date

Wed, 26/03/2014 - 12:00pm

Venue

RC-4082, The Red Centre, UNSW