1,866 research outputs found
Local calibrations for minimizers of the Mumford-Shah functional with a triple junction
We prove that, if u is a function satisfying all Euler conditions for the
Mumford-Shah functional and the discontinuity set of u is given by three line
segments meeting at the origin with equal angles, then there exists a
neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah
functional on U with respect to its own boundary conditions on the boundary of
U. The proof is obtained by using the calibration method.Comment: 28 pages, 4 figure
Relaxation of the Hencky model in perfect plasticity
In this paper we give a full proof of the relaxation of the Hencky model in
perfect plasticity, under suitable assumptions for the domain and the Dirichlet
boundary
Functionals depending on curvatures with constraints
We deal with a family of functionals depending on curvatures and we prove for
them compactness and semicontinuity properties in the class of closed and
bounded sets which satisfy a uniform exterior and interior sphere condition. We
apply the results to state an existence theorem for the Nitzberg and Mumford
problem under this additional constraint.Comment: 20 pages. To appear on Rendiconti del Seminario Matematico
dell'Universita' di Padov
Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set
Using a calibration method, we prove that, if w is a function which satisfies
all Euler conditions for the Mumford-Shah functional on a two-dimensional
domain, and the discontinuity set S of w is a regular curve connecting two
boundary points, then there exists a uniform neighbourhood U of S such that w
is a minimizer of the Mumford-Shah functional on U with respect to its own
boundary conditions. We show that Euler conditions do not guarantee in general
the minimality of w in the class of functions with the same boundary value of w
and whose extended graph is contained in a neighbourhood of the extended graph
of w, and we give a sufficient condition in terms of the geometrical properties
of the domain and the discontinuity set under which this kind of minimality
holds.Comment: 31 pages, 2 figure
Finite Difference Approximation of Free Discontinuity Problems
We approximate functionals depending on the gradient of and on the
behaviour of near the discontinuity points, by families of non-local
functionals where the gradient is replaced by finite differences. We prove
pointwise convergence, -convergence, and a compactness result which
implies, in particular, the convergence of minima and minimizers.Comment: 39 pages. to appear on Proc. Royal Soc. Edinb. Ser.
The time-dependent von Kármán plate equation as a limit of 3D nonlinear elasticity
The asymptotic behaviour of the solutions of three-dimensional
nonlinear elastodynamics in a thin plate is studied, as the thickness h of the
plate tends to zero. Under appropriate scalings of the applied force and of the
initial values in terms of h, it is shown that three-dimensional solutions of the
nonlinear elastodynamic equation converge to solutions of the time-dependent
von Kármán plate equation
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