The calibration method for the Mumford-Shah functional and free-discontinuity problems
Giovanni Alberti, Guy Bouchitte', Gianni Dal Maso
TL;DR
This paper introduces a minimality criterion for the Mumford-Shah functional and similar non-convex variational problems, simplifying proofs of minimality results in free-discontinuity problems.
Contribution
It provides a new, streamlined method for establishing minimality in Mumford-Shah and related variational integrals, enhancing theoretical understanding.
Findings
Minimality criterion for Mumford-Shah functional established
Simplified proofs for multiple minimality results
Applicable to a broad class of non-convex variational problems
Abstract
In this paper we present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems