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Variational Problems with a Free Discontinuity Set
1994The present chapter is a short survey about the most recent contributions to the mathematical analysis of a variational approach to image segmentation proposed by D. Mumford and J. Shah.
LEACI, Antonio, S. SOLIMINI
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Discontinuous free-form lens design for prescribed irradiance
Applied Optics, 2007For the problem of point source forming prescribed irradiance, a new, to the best of our knowledge, method-variable separation mapping method is presented, which establishes separately the correspondence between variables on the light source and the target plane.
Lin, Wang, Keyuan, Qian, Yi, Luo
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Lower Semicontinuity Properties of Functionals with Free Discontinuities
Archive for Rational Mechanics and Analysis, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francesco Maddalena, Sergio Solimini
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Second Order Variational Problems with Free Discontinuity and Free Gradient Discontinuity
2004In this contribution we unify general properties of functionals depending on first and second derivatives together with free discontinuities and free gradient discontinuities. The analysis includes many relevant applications to image segmentation and continuum mechanics.
CARRIERO, Michele +2 more
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Regularity of the Free Discontinuity Set
2000Abstract In this chapter we study the partial regularity of the discontinuity set of the quasi minimisers of the functional.
Luigi Ambrosio +2 more
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Functions of Bounded Variation and Free Discontinuity Problems
2000Abstract This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. The aim of this book is twofold: The first three chapters present all the basic prerequisites for the treatment of free discontinuity ...
AMBROSIO, Luigi, FUSCO N., PALLARA D.
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Plastic free discontinuities and special bounded Hessian
1992A model for an elastic-plastic thin plate is studied by minimizing a suitable functional or displacements with special bounded Hessian. The existence of equilibrium for the weak formulation of Neumann, Dirichlet and obstacle problems is stated together with some properties of the free gradient discontinuity set and some relationships with the strong ...
M. CARRIERO +2 more
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On the approximation of free discontinuity problems
1992This paper compliments another one of the authors [Commun. Pure Appl. Math. 43, No. 8, 999-1036 (1990; Zbl 0722.49020)] both concerning the approximation (in the sense of \(\Gamma\)-convergence) of the Mumford-Shah type functional (or rather its lower semicontinuous envelope) by elliptic functionals which formally have simpler form.
AMBROSIO L, TORTORELLI, VINCENZO MARIA
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Partial regularity of free discontinuity sets. I
1997The authors consider a class of perturbations of the functional \[ F(u,K)=\int_{\Omega\setminus K}|\nabla u|^2dx+{\mathcal H}^{n-1}(K) \] where \(\Omega\in\mathbb{R}^n\) is an open set, \(K\) is a variable closed subset of \(\Omega\), \(u\) is a smooth (\(C^1\)) function outside \(K\) and \({\mathcal H}^{n-1}\) stands for the \((n-1)\)-dimensional ...
AMBROSIO, Luigi, Pallara D.
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Motion of Free Particles in Discontinuous Gravitational Fields
American Journal of Physics, 1959A new paradox occurring in the usual solution of the original “clock paradox” is given a natural physical interpretation by the observation that the mass of a particle moving in a gravitational field depends on the gravitational potential as well as on the velocity, thus changing abruptly when a gravitational field is suddenly turned off.
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