On boundary regularity for Plateau's problem

Plateaus' problem for parametric double integrals: I. Existence and regularity in the interior

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

Boundary regularity for a parabolic obstacle type problem

Mathematical background: The regularity of free boundaries has been extensively studied over the last thirty years and the literature on the Stefan problem is vast. This problem however (that is, the Stefan problem without sign restriction) was, to the author’s knowledge, first studied by L. A. Caffarelli, A. Petrosyan and H. Shahgholian in [CPS]. The authors of [CPS] showed that a solution is ...

Boundary Regularity and the Dirichlet Problem for Harmonic Maps

In a previous paper [10] we developed an interior regularity theory for energy minimizing harmonic maps into Riemannian manifolds. In the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed Dirichlet boundary condition. We show that such maps are regular in a full neighborhood of the boundary, assuming appropriate regularity on the manifolds,...

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.