5 papers · 1 filter
Existence and local asymptotics for a system of cross-diffusion equations with nonlocal Cahn-Hilliard terms
Elisa Davoli, Greta Marino, Jan-Frederik Pietschmann
We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric sing…
Local asymptotics for the nonlocal Swift-Hohenberg equation
Elisa Davoli, Christian Kuehn, Luca Scarpa +1
The nonlocal-to-local asymptotics investigation for evolutionary problems is a central topic both in the theory of PDEs and in functional analysis. More recently, it became the mai…
On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case
Stefano Almi, Elisa Davoli, Anna Kubin +1
We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient…
Non-local non-homogeneous phase transitions: regularity of optimal profiles and sharp-interface limit
Elisa Davoli, Emanuele Tasso
We provide a novel sharp-interface analysis via Gamma-convergence for a non-local and non-homogeneous diffuse-interface model for phase transitions, featuring an interplay between…
Existence results for Cahn-Hilliard type systems driven by nonlocal integrodifferential operators with singular kernels
Elisa Davoli, Chiara Gavioli, Luca Lombardini
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and with a possibly singular potential. We first focus on the case of homogeneous Dirich…