On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres

For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are C 1,α. We recover the regularity results of Caffarelli for

Under the restriction 2 m 4, we prove the full Hölder regularity of weakly harmonic maps (i.e., weak solutions of its Euler–Lagrange equation) from M to N in the case that the

stationary minimal surfaces in a higher dimensional manifold we may as well consider the situation where the supporting submanifold has

Analogous boundary regularity questions for solutions of the nonpara- metric least area problem were studied by Simon [14]. 2) arises in a similar fashion as for

cannot work in the general case due to the inexistence of a nice parametrix for hyperbolic equations near the boundary.. The parametrix approach is,

BELL, Proper holomorphic mappings and the Bergman kernel function,

PIN010DUK, Proper holomorphic mappings of strictly pseudoconvex domains, (Russian), Dokl. 1; English translation

In this paper we determine the differentiability properties of the conformal representation of the surface restricted to that are V in the boundary of the