Calculus of Variations and Geometric Measure Theory

E. Davoli - L. Scarpa - L. Trussardi

Local asymptotics for nonlocal convective Cahn-Hilliard equations with $W^{1,1}$ kernel and singular potential

created by davoli on 28 Nov 2019
modified on 16 Apr 2021


Accepted Paper

Inserted: 28 nov 2019
Last Updated: 16 apr 2021

Journal: Journal of Differential Equations
Year: 2021


We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a $W{1,1} convolution kernel and under homogeneous Neumann conditions. Any type of potential, possibly also of double-obstacle or logarithmic type, is included. Additionally, we highlight variants and extensions to the setting of periodic boundary conditions and viscosity contributions, as well as connections with the general theory of evolutionary convergence of gradient flows.