4 papers · 1 filter
Solid-solid phase transitions with space-dependent wells
Elisa Davoli, Jakob Deutsch, Manuel Friedrich +1
We investigate a second-order Modica-Mortola functional of the form \[ E_\varepsilon[u] := \int_Ω\frac{1}{\varepsilon} W(x, \nabla u) + \varepsilon|\nabla^2 u|^2 \, dx, \] which mo…
A regularity result for
Jakob Deutsch, Samuele Riccò
It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space on bounded domains with boundary. In this work, w…
Low regularity potentials in heterogeneous Cahn--Hilliard functionals
Riccardo Cristoferi, Jakob Deutsch, Luca Pignatelli
In this paper, we study the prototypical model of liquid-liquid phase separation, the Cahn-Hilliard functional, in a highly irregular setting. Specifically, we analyze potentials w…
A note on the recovery sequence in the double gradient model for phase transitions
Jakob Deutsch
We investigate the inequality in the double gradient model for phase transitions governed by a Modica--Mortola functional with a double-well potential in two dimensions.…