9 results
Search Results
Now showing 1 - 9 of 9
- ItemA Widder's type theorem for the heat equation with nonlocal diffusion(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Barrios, Begoña; Peral, Ireneo; Soria, Fernando; Valdinoci, EnricoI
- ItemGradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Cozzi, Matteo; Farina, Alberto; Valdinoci, EnricoWe consider the Wulff-type energy functional where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate, quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.
- ItemUniqueness and nondegeneracy of positive solutions of (-Delta) su + u = up in RN when s is close to 1(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fall, Mouhamed Moustapha; Valdinoci, EnricoWe consider the equation (-Δ)s u+u = up with s ∈ (0,1) in the subcritical range of p. We prove that if s is sufficiently close to 1 the equation possesses a unique minimizer, which is nondegenerate.
- ItemDislocation dynamics in crystals: A macroscopic theory in a fractional Laplace setting(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dipierro, Serena; Palatucci, Giampiero; Valdinoci, EnricoWe consider an evolution equation arising in the PeierlsNabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. these dislocation points evolve according to the external stress and an interior repulsive potential.
- ItemStrongly nonlocal dislocation dynamics in crystals(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dipierro, Serena; Figalli, Alessio; Valdinoci, EnricoWe consider an equation motivated by crystal dynamics and driven by a strongly nonlocal elliptic operator of fractional type. We study the evolution of the dislocation function for macroscopic space and time scales, by showing that the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. We also prove that the motion of these dislocation points is governed by an interior repulsive potential that is superposed to an elastic reaction to the external stress.
- ItemGevrey regularity for integro-differential operators(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Albanese, Guglielmo; Fiscella, Alessio; Valdinoci, EnricoWe prove a regularity theory in the Gevrey class for a family of nonlocal differential equations of elliptic type.
- ItemMinimization of a fractional perimeter-Dirichlet integral functional(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Caffarelli, Luis; Savin, Ovidiu; Valdinoci, EnricoWe consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set. We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis, density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.
- ItemRegularity and Bernstein-type results for nonlocal minimal surfaces(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Figalli, Alessio; Valdinoci, EnricoWe prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi [5] stating that the validity of Bernsteins theorem in dimension n + 1 is a consequence of the nonexistence of n-dimensional singular minimal cones in IRn.
- ItemA critical Kirchhoff type problem involving a non-local operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Fiscella, Alessio; Valdinoci, EnricoWe show the existence of non-negative solutions for a Kirchhoff type problem driven by a non-local integrodifferential operator.