Special Lecture: Charles Martin (UCSB), 'Variational Methods in Potential Theory and Planar Elliptic Growth'

Event Date: 

Wednesday, June 5, 2013 - 11:00am to 12:00pm

Event Location: 

  • 6635 South Hall

Event Contact: 

Charles Martin

Email: cmart07@math.ucsb.edu

Abstract: A domain in the plane is said to undergo a Laplacian growth process when its boundary velocity is given by the outward normal derivative of the Green function (for the Laplace operator). LG models
many physical processes and possesses nice properties, but in some situations one might want to include inhomogeneities in the underlying plane; the resulting model replaces the Green function of the Laplace
operator with that of a more general elliptic operator, and as such is called elliptic growth. Viewing the new operator as a perturbation of the Laplacian, we will develop first order variational formulas for the Green
function and its normal derivative. With these formulas we can show that the space of resulting corrections to the boundary velocity is dense in L^2 of the boundary.