Calculus of Variations and Geometric Measure Theory

P. W. Dondl - M. Novaga - B. Wirth - S. Wojtowytsch

A Phase-field Approximation of the Perimeter under a Connectedness Constraint

created by novaga on 14 Oct 2018
modified on 01 Jan 2022


Published Paper

Inserted: 14 oct 2018
Last Updated: 1 jan 2022

Journal: SIAM J. Math. Anal.
Volume: 51
Number: 5
Pages: 3902–3920
Year: 2019

ArXiv: 1810.05787 PDF


We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional. We prove convergence of the approximating energies and present numerical results and applications to image segmentation.