Calculus of Variations and Geometric Measure Theory

E. Davoli - H. Ranetbauer - L. Scarpa - L. Trussardi

Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics

created by davoli on 12 Feb 2019
modified on 04 Sep 2020


Published Paper

Inserted: 12 feb 2019
Last Updated: 4 sep 2020

Journal: Annales de l'Institut Henri Poincare. Analyse Non Lineaire
Year: 2019


Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations with degenerate potential is shown. The nonlocality is described by means of a symmetric singular kernel not falling within the framework of any previous existence theory. A convection term is also taken into account. Building upon this novel existence result, we prove convergence of solutions for this class of nonlocal Cahn-Hilliard equations to their local counterparts, as the nonlocal convolution kernels approximate a Dirac delta. Eventually, we show that, under suitable assumptions on the data, the solutions to the nonlocal Cahn-Hilliard equations exhibit further regularity, and the nonlocal-to-local convergence is verified in a stronger topology.