Fanghua Lin, Courant Institute, NYU
Energy minimizing harmonic maps from a three-ball into the two-sphere are well understood. A natural existence question for a continuous harmonic map with a suitably given Dirichlet boundary value or in a given homotopic class [a problem that I learned from R.Schoen in mid-80s] remains open.…
Nicola Garofalo, University of Padova, Italy & Arizona State University
A basic problem in analysis is the Dirichlet problem for the Laplacian in the upper half-space. It is a classical fact that the trace of the Neumann derivative of the solution equals the half-Laplacian of the boundary datum. In a seminal 2007 paper…