Calculus of Variations and Geometric Measure Theory
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P. W. Dondl - M. Novaga - B. Wirth - S. Wojtowytsch

Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields

created by novaga on 14 Oct 2018
modified on 22 Oct 2018


Submitted Paper

Inserted: 14 oct 2018
Last Updated: 22 oct 2018

Year: 2018

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.


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