5 papers
A two-dimensional Allen-Cahn theory for interfaces with boundary
Marco Badran, Manuel del Pino, Marco A. M. Guaraco
We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model solut…
Uniform small energy regularity for fractional geometric problems
Marco Badran, Giacomo Cozzi
We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range , answering a question posed by Hyder, Segatti, Sire and Wa…
Nonlocal free boundary minimal surfaces
Marco Badran, Serena Dipierro, Enrico Valdinoci
We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain of as the (boundaries of) critical points of the fract…
Stationary -harmonic maps approaching planar singular harmonic maps to the circle
Marco Badran, Jean Van Schaftingen
Given a bounded planar domain , we show that any singular harmonic map into the circle corresponding to a topologically nondegenerate critica…
Harmonic maps to the circle with higher dimensional singular set
Marco Badran
In a closed, oriented ambient manifold we consider the problem of finding -valued harmonic maps with prescribed singular set. We show that the boundary of a…