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We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single...
We recently derived a very general representation formula
for the boundary voltage perturbations caused by internal
conductivity inhomogeneities of low volume fraction (
cf. Capdeboscq and Vogelius (2003)). In this paper we show how this
representation formula may be used to obtain very
accurate estimates for the size of the inhomogeneities
in terms of multiple boundary measurements. As demonstrated
by our computational experiments, these estimates are significantly
better than previously known...
We study the potential which minimizes the fundamental gap of the
Schrödinger operator under the total mass constraint. We consider
the relaxed potential and prove a regularity result for the optimal
one, we also give a description of it. A consequence of this result
is the existence of an optimal potential under L1 constraints.
An optimal part of the boundary of a plane domain for the Poisson equation with mixed boundary conditions is to be found. The cost functional is (i) the internal energy, (ii) the norm of the external flux through the unknown boundary. For the numerical solution of the state problem a dual variational formulation - in terms of the gradient of the solution - and spaces of divergence-free piecewise linear finite elements are used. The existence of an optimal domain and some convergence results are...
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