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• W212404744 abstract "Regularity properties for (local) 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 80s 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 in W -(i?;R) of the functional are Holder continuous of any exponent ~y€(0.1). where !7cR is an open, bounded set, / is a (not necessarily convex) function growing linearly at infinity, and v{u) stands for the vector of all 2x2 minors of Du. As a consequence, it is possible to obtain existence of classical in SBV(QM) of where g€L(f2-M). q>. /3,-y>0 These are ''classical minimizers in the sense that /f((5T5u)nr?)=0 and U61V 1 (J?sT). 1991 Mathematics subject classification (Amer. Math. Soc): 35J20. 49Q20. 49J45. 49N60" @default.
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• W212404744 date "1997-01-01" @default.
• W212404744 modified "2023-09-25" @default.
• W212404744 title "Regularity of minimizers for a class of membrane energies" @default.
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