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math.AP2020
On nonlocal minimal graphs
Matteo Cozzi, Luca Lombardini
We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison prin…
math.AP2020
An elliptic boundary value problem with fractional nonlinearity
Nicola Abatangelo, Matteo Cozzi
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect t…
math.AP2020★ 1 cited
A fractional Michael-Simon Sobolev inequality on convex hypersurfaces
Xavier Cabre, Matteo Cozzi, Gyula Csató
The classical Michael-Simon and Allard inequality is a Sobolev inequality for functions defined on a submanifold of Euclidean space. It is governed by a universal constant independ…