The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 61 –
80 of
119
We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli.
We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised Reverse...
In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not
preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a
scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in
addition that the only normal variations which preserve the regularity are those with constant magnitude.
This...
An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...
We consider the question raised in [1] of whether relaxed energy
densities involving both bulk and surface energies
can be written as a sum of two functions, one depending on the net gradient
of admissible functions, and the other on net
singular part.
We show that, in general, they cannot. In particular, if the bulk density
is quasiconvex but not convex, there
exists a convex and homogeneous of degree 1 function of the jump such that
there is no such representation.
Currently displaying 61 –
80 of
119