Results 221 to 230 of about 590,396 (265)

Free-discontinuity problems: calibration and approximation of solutions

, 2001
openaire   +1 more source

Strong Existence for Free Discontinuity Problems in Linear Elasticity

SIAM Journal on Mathematical Analysis
In this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in linear elasticity with anisotropic, cohesive, or heterogeneous behavior ...
Manuel Friedrich, Camille Labourie, Kerrek Stinson   +2 more
semanticscholar   +3 more sources

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Approximation of Free-Discontinuity Problems

, 1998
Andrea Braides
semanticscholar   +2 more sources

Homogenization of free discontinuity problems

Archive for Rational Mechanics and Analysis, 1996
Following Griffith's theory, hyperelastic brittle media subject to fracture can be modeled by the introduction, in addition to the elastic volume energy, of a surface term which accounts for crack initiation. In its simplest formulation, the energy of a deformation \(u\) is of the form \[ E(u, K)=\int_{\Omega\setminus K}f(\nabla u)dx+ \lambda{\mathcal ...
Andrea Braides, A. Defranceschi, E. Vitali   +2 more
semanticscholar   +5 more sources

Relaxation results for some free discontinuity problems.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1995
In many problems of Mathematical Physics one is concerned with minimum problems for functions defined on function spaces allowing discontinuities. When the discontinuity set is not a priori given the problem is called with ``free discontinuity'' and it would be helpful, for the existence theory and for the study of minimizing sequences, the knowledge ...
G. Bouchitté, G. Buttazzo, Andrea Braides   +2 more
semanticscholar   +2 more sources

Nonlocal Approximation of Nonisotropic Free-Discontinuity Problems

SIAM Journal on Applied Mathematics, 1999
A large class of problems in fracture mechanics, image segmentation, liquid cristals theory can be formulated as ``free-discontinuity problems'' in which one looks for the minimum of integral functionals of the form: \[ \int_{\Omega}g(x,\nabla u) dx + \int_{S_u}\varphi(x,[u],\nu_u) d{\mathcal{H}}^{n-1}, \] where \(\Omega\) is an open and bounded set in
G. Cortesani, Rodica Toader
semanticscholar   +3 more sources

Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022
We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient.
R. Marziani, Francesco Solombrino
semanticscholar   +1 more source

REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS

Mathematical Models and Methods in Applied Sciences, 2000
We consider a class of smooth local nonconvex functionals defined on W2,2(Ω), depending on a small parameter ε and we prove that they converge, as ε tends to 0, to a functional F(u,Ω) with a bulk density depending on the gradient of u and a surface energy concentrated on the jump set of u.
G. Bouchitté, C. Dubs, P. Seppecher
semanticscholar   +3 more sources