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.


Andrew Morris

Research Area

University of Oxford


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


RC-4082, The Red Centre, UNSW