3 papers
math.AP2026
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…
math.AP2026
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…
math.AP2025
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.…