107 citations · 369 across the 19 of their papers we have counts for
23 papers
A half-space theorem for nonlocal minimal surfaces
Matteo Cozzi, Jack Thompson
We establish a half-space theorem à la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.
A fractional De Giorgi isoperimetric type inequality
Matteo Cozzi, Tomás Sanz-Perela
We establish an isoperimetric type inequality for the level sets of functions in fractional Sobolev spaces. This answers a question posed by the first author in a previous paper. T…
Global gradient regularity and a Hopf lemma for quasilinear operators of mixed local-nonlocal type
Carlo Alberto Antonini, Matteo Cozzi
We address some regularity issues for mixed local-nonlocal quasilinear operators modeled upon the sum of a -Laplacian and of a fractional -Laplacian. Under suitable assu…
A quantitative version of the Gidas-Ni-Nirenberg Theorem
Giulio Ciraolo, Matteo Cozzi, Matteo Perugini +1
A celebrated result by Gidas, Ni & Nirenberg asserts that classical positive solutions to semilinear equations in a ball vanishing at the boundary must be radial and…
Non-uniqueness for the nonlocal Liouville equation in and applications
Luca Battaglia, Matteo Cozzi, Antonio J. Fernández +1
We construct multiple solutions to the nonlocal Liouville equation \begin{equation} \label{eqk} \tag{L} (-Δ)^{\frac{1}{2}} u = K(x) e^u \quad \mbox{ in } \mathbb{R}. \end{equation}…
Blowing-up solutions for a nonlocal Liouville type equation
Matteo Cozzi, Antonio J. Fernández
We consider the nonlocal Liouville type equation $$ (-Δ)^{\frac{1}{2}} u = \varepsilon κ(x) e^u, \quad u > 0, \quad \mbox{in } I, \qquad u = 0, \quad \mbox{in } \mathbb{R} \setminu…