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4 papers
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…
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…
Long-time asymptotics for evolutionary crystal dislocation models
Matteo Cozzi, Juan Dávila, Manuel del Pino
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equation…
On the growth of nonlocal catenoids
Matteo Cozzi, Enrico Valdinoci
As well known, classical catenoids in possess logarithmic growth at infinity. In this note we prove that the case of nonlocal minimal surfaces is significantly dif…