Free boundary regularity for almost-minimizers

Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals

We give a new proof of the small excess regularity theorems for integer multiplicity recti able currents of arbitrary dimension and codimension minimizing an elliptic parametric variational integral. This proof does not use indirect blow-up arguments, it covers interior and boundary regularity, it applies to almost minimizing currents, and it gives an explicit and often optimal modulus of conti...

Partial Regularity for Almost Minimizers of Quasi-Convex Integrals

We consider almost minimizers of variational integrals whose integrands are quasiconvex. Under suitable growth conditions on the integrand and on the function determining the almost minimality, we establish almost everywhere regularity for almost minimizers and obtain results on the regularity of the gradient away from the singular set. We give examples of problems from the calculus of variatio...

Partial regularity for quasi minimizers

Analytic regularity of a free boundary problem

In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most n− 8. Mathematics Subject Classification (2000): 49Q20

Free boundary regularity for harmonic measures and Poisson kernels

One of the basic aims of this paper is to study the relationship between the geometry of “hypersurface like” subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling properties of a measure determine the geometry of its support. A Radon measure is said to be doubling with constant C if C times the measure of the ball of radius r c...