Calculus of Variations and Geometric Measure Theory

M. Carriero - A. Leaci - F. Tomarelli

A Dirichlet problem with free gradient discontinuity

created by leaci on 24 Jun 2009
modified on 20 Dec 2010


Published Paper

Inserted: 24 jun 2009
Last Updated: 20 dec 2010

Journal: Adv. Math. Sci. Appl.
Volume: 20
Number: 1
Pages: 107-141
Year: 2010


We prove the existence of strong solution for Blake & Zisserman functional under Dirichlet boundary condition. The result is obtained by showing partial regularity of weak solutions up to the boundary through blow-up technique and a decay property for bi-harmonic functions in half disk.

Keywords: calculus of variations, Regularity of weak solution, Free discontinuity problem, Image segmentation