2001/05/08 by Maria Giovanna Mora, Mora, Maria Giovanna
Mathematics · #49K10 (49Q20) #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:49K10
paper · pdf · doi:10.48550/arxiv.math/0105057
28 pages, 4 figures
arxiv created 2001/05/09 · arxiv updated 2009/11/30
We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.