4 papers
Asymptotics as of the nonlocal nonparametric Plateau problem with obstacles
Claudia Bucur, Luca Lombardini
In this paper, we introduce a functional and a geometric setting for an obstacle problem for nonlocal minimal graphs. In particular we study existence of solutions, a priori estima…
Nonlocal Micromagnetics: Compactness Criteria, Existence of Minimizers, and Brown's Fundamental Theorem
Giovanni Di Fratta, Rossella Giorgio, Luca Lombardini
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered e…
Existence results for Cahn-Hilliard type systems driven by nonlocal integrodifferential operators with singular kernels
Elisa Davoli, Chiara Gavioli, Luca Lombardini
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and with a possibly singular potential. We first focus on the case of homogeneous Dirich…
Continuity of s-minimal functions
Claudia Bucur, Serena Dipierro, Luca Lombardini +1
We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient an…