Roger Moser

A HIGHER ORDER ASYMPTOTIC PROBLEM RELATED TO PHASE TRANSITIONS

An asymptotic analysis of a family of functionals used in the van der Waals--Cahn--Hilliard theory of phase transitions gives rise to a generalized area functional in the limit. We examine a family of related higher order functionals on a three-dimensional domain. The expected limit in this case is a generalization of the Willmore functional. An analysis of the problem under a monotonicity assumption supports this conjecture.

The inverse mean curvature flow and p-harmonic functions

We consider the level set formulation of the inverse mean curvature flow. We establish a connection to the problem of

Ginzburg-Landau vortices for thin ferromagnetic films

p

A Variational Problem Pertaining to Biharmonic Maps

-harmonic functions and give a new proof for the existence of weak solutions.

An

We generalize the asymptotic analysis of Bethuel, Brezis, and Helein (1994) for Ginzburg-Landau functionals to a model for thin films of ferromagnetic materials.

L^p

The second derivative of a map into a Riemannian manifold is given by a nonlinear differential operator. We study minimizers and critical points of the L 2-norm of this second derivative. We show existence of minimizers with the direct method and we prove a partial regularity result.

regularity theory for harmonic maps

Motivated by the harmonic map heat flow, we consider maps between Riemannian manifolds such that the tension field belongs to an Lp-space. Under an appropriate smallness condition, a certain degree of regularity follows. For suitable solutions of the harmonic map heat flow, we have a partial regularity result as a consequence.

Vortex motion for the Landau-Lifshitz-Gilbert equation with spin transfer torque

We study the Landau–Lifshitz–Gilbert equation for the dynamics of a magnetic vortex system. We include the spin-torque effects of an applied spin current, and we rigorously derive an equation of motion (“Thiele equation”) for vortices if the current is not too large. Our method of proof strongly utilizes the geometry of the problem in order to obtain the necessary energy estimates.

Weak solutions of a biharmonic map heat flow

Abstract The equation studied in this paper is one of several fourth order analogues of the harmonic map heat flow. For up to 8-dimensional domains, the problem permits the construction of weak solutions with a time discretization method.

Unique solvability of the Dirichlet problem for weakly harmonic maps

Abstract: We prove existence and uniqueness of weakly harmonic maps from the unit ball in ℝn (with n≥ 3) to a smooth compact target manifold within the class of maps with small scaled energy for suitable boundary data.