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Acerbi, Fonseca and Fusco 1 REGULARITY OF MINIMIZERS
 

Summary: Acerbi, Fonseca and Fusco 1
REGULARITY OF MINIMIZERS
FOR A CLASS OF MEMBRANE ENERGIES
Emilio Acerbi 1
Irene Fonseca 2
Nicola Fusco 3
Abstract Regularity properties for (local) minimizers of elastic energies have been challenging
mathematical techniques for many years. Recently the interest has resurfaced due in part to
the fact that existing partial regularity results do not suffice to ensure existence of (classical)
solutions to problems involving free discontinuity sets. The analysis of such questions was
started with the fundamental work of De Giorgi in the early 80's in connection with the
Mumford-Shah model for image segmentation in computer vision, and later applied to some
models for fracture mechanics, thin films, and membranes ([1], [18], [20]). In this paper it is
shown that local minimizers in W1,2
(; Rd
) of the functional
F0(u, ) :=

1
2

  

Source: Acerbi, Emilio - Dipartimento di Matematica, UniversitÓ degli Studi di Parma

 

Collections: Mathematics