existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...
This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.