Results 231 to 240 of about 590,396 (265)
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Smooth and Broken Minimizers of Some Free Discontinuity Problems
, 2017We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data. We examine in detail two examples: the elastic-plastic beam and the elastic-plastic plate with free yield lines.
D. Percivale, F. Tomarelli
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Free-discontinuity problems generated by singular perturbation
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1998We show that some free discontinuity problems can be obtained as a limit of nonconvex local functionals with a singular perturbation of higher order.
R. Alicandro, Andrea Braides, M. Gelli
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Monotonicity Formula and Regularity for General Free Discontinuity Problems
Archive for Rational Mechanics and Analysis, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bucur, Dorin, Stephan, Luckhaus
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Sequences of Singularly Perturbed Functionals Generating Free-Discontinuity Problems
SIAM Journal on Mathematical Analysis, 2003This is a very interesting paper. From the Introduction: ``Many models in the fields of fracture mechanics and computer vision lead to free-discontinuity problems, that is, to the minimization of functionals defined in spaces of discontinuous functions (namely, BV and SBV) involving energies with a bulk part and a surface part concentrated along the ...
M. Morini
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Calculus of Variations and Partial Differential Equations, 2018
We present a compactness result in the space $$GSBV^p$$GSBVp which extends the classical statement due to Ambrosio (Arch Ration Mech 111:291–322, 1990) to problems without a priori bounds on the functions.
Manuel Friedrich
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We present a compactness result in the space $$GSBV^p$$GSBVp which extends the classical statement due to Ambrosio (Arch Ration Mech 111:291–322, 1990) to problems without a priori bounds on the functions.
Manuel Friedrich
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FREE DISCONTINUITY PROBLEMS WITH UNBOUNDED DATA
Mathematical Models and Methods in Applied Sciences, 1994We prove the existence of a minimizing pair for a free discontinuity problem, i.e. a variational problem in which the unknowns are a closed set K and a function suitably smooth outside K. Examples of such problems come from pattern recognition and mathematical physics, when both “volume” energy and “surface” energy are present.
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Sequences of Non‐Local Functionals Which Approximate Free‐Discontinuity Problems
Archive for Rational Mechanics and Analysis, 1998The aim of the paper is to develop a general method for the approximation, in the sense of \(\Gamma\)-convergence, of free discontinuity problems \[ \min\biggl\{ \int_\Omega g(x,\nabla u) dx+\int_{S_u\cap\Omega} \varphi(x,[u],\nu_u) d{\mathcal H}^{n-1}: u\in \text{SBV}(\Omega)\biggr\} \] (here \(S_u\) is the approximate discontinuity set, \([u]\) is ...
G. Cortesani
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Minimisers of Free Discontinuity Problems
2000Abstract In this chapter and in the next one we study existence and regularity of solutions of a class of free discontinuity problems whose model is the Mumford-Shah functional introduced in Chapter 4.
Luigi Ambrosio +2 more
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Discrete approximation of a free discontinuity problem
Numerical Functional Analysis and Optimization, 1994We approximate by discrete Г-convergence a functional proposed by Mumford-Shah for a variational approach to image segmentation. Such a functional is first relaxed with a sequence of nonconvex functionals, which in turn, are dis-cretized by piecewise linear finite elements. Under a suitable relation between the relaxation parameter ∊and the meshsize h,
BELLETTINI, GIOVANNI, Coscia, A.
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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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