5 papers
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…
Minimisers of a fractional seminorm and nonlocal minimal surfaces
Claudia Bucur, Serena Dipierro, Luca Lombardini +1
The recent literature has intensively studied two classes of nonlocal variational problems, namely the ones related to the minimisation of energy functionals that act on functions…
Minimization problems involving nonlocal functionals: nonlocal minimal surfaces and a free boundary problem
Luca Lombardini
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the -fractional perimeter and its m…
Bernstein-Moser-type results for nonlocal minimal graphs
Matteo Cozzi, Alberto Farina, Luca Lombardini
We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of cla…
Fractional perimeter from a fractal perspective
Luca Lombardini
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimen…