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1999 Higher regularity of solutions of free discontinuity problems
Luigi Ambrosio, Nicola Fusco, Diego Pallara
Differential Integral Equations 12(4): 499-520 (1999).

Abstract

In this paper we continue the analysis, started in [6],[7], of the regularity of solutions of free discontinuity problems. We choose as a model problem the minimization of the Mumford-Shah functional. Assuming that in some region the optimal discontinuity set $\Gamma$ is the graph of a $C^{1,\rho}$ function, we look for conditions ensuring the higher regularity of $\Gamma$. Our results are optimal in the two dimensional case. As an application, we prove that in the case of the Mumford-Shah functional and in similar problems the Lavrentiev phenomenon does not occur.

Citation

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Luigi Ambrosio. Nicola Fusco. Diego Pallara. "Higher regularity of solutions of free discontinuity problems." Differential Integral Equations 12 (4) 499 - 520, 1999.

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1007.49025
MathSciNet: MR1697242

Subjects:
Primary: 49N60
Secondary: 35R35, 49K20

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.12 • No. 4 • 1999
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