3,570 research outputs found
Self-similar minimizers of a branched transport functional
We solve here completely an irrigation problem from a Dirac mass to the
Lebesgue measure. The functional we consider is a two dimensional analog of a
functional previously derived in the study of branched patterns in type-I
superconductors. The minimizer we obtain is a self-similar tree.Comment: Indiana University Mathematics Journal, Indiana University
Mathematics Journal, In pres
Equilibrium shapes of charged droplets and related problems: (mostly) a review
We review some recent results on the equilibrium shapes of charged liquid
drops. We show that the natural variational model is ill-posed and how this can
be overcome by either restricting the class of competitors or by adding
penalizations in the functional. The original contribution of this note is
twofold. First, we prove existence of an optimal distribution of charge for a
conducting drop subject to an external electric field. Second, we prove that
there exists no optimal conducting drop in this setting
Volume-constrained minimizers for the prescribed curvature problem in periodic media
We establish existence of compact minimizers of the prescribed mean curvature
problem with volume constraint in periodic media. As a consequence, we
construct compact approximate solutions to the prescribed mean curvature
equation. We also show convergence after rescaling of the volume-constrained
minimizers towards a suitable Wulff Shape, when the volume tends to infinity.Comment: In this version the statement of Lemma 2.5 has been corrected with
respect to the published versio
Phase segregation for binary mixtures of Bose-Einstein Condensates
We study the strong segregation limit for mixtures of Bose-Einstein
condensates modelled by a Gross-Pitaievskii functional. Our first main result
is that in presence of a trapping potential, for different intracomponent
strengths, the Thomas-Fermi limit is sufficient to determine the shape of the
minimizers. Our second main result is that for asymptotically equal
intracomponent strengths, one needs to go to the next order. The relevant limit
is a weighted isoperimetric problem. We then study the minimizers of this limit
problem, proving radial symmetry or symmetry breaking for different values of
the parameters. We finally show that in the absence of a confining potential,
even for non-equal intracomponent strengths, one needs to study a related
isoperimetric problem to gain information about the shape of the minimizers
The Impact of Public Health Policy: The Case of Community Health Centers
The aim of this paper is to assess the impact of the Community Health Center (CHC) on health levels in the U.S. Using infant mortality as the underlying health indicator, a time series of large counties as the data set, and multivariate regression techniques, we investigate the extent to which the presence of a program in a county affects future mortality. We find that CHCs have negative and statistically significant impacts on white and black infant mortality rates.The centers have larger effects on black infant mortality than on white infant mortality. The reduction in the black infant mortality rate between 1970 and 1978 due to the CHC system amounts to one death per thousand live births or approximately 12 percent of the observed decline.This result is particularly striking in light of the well-known higher infant mortality rate of blacks. A reduction in the excess mortality rate of black babies has been dentfied as a goal of public health policy for a number of years. Our results suggest that community health centers have the potential to make a substantial contribution to the achievement of this goal.
The -limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension
In this paper we generalize to arbitrary dimensions a one-dimensional
equicoerciveness and -convergence result for a second derivative
perturbation of Perona-Malik type functionals. Our proof relies on a new
density result in the space of special functions of bounded variation with
vanishing diffuse gradient part. This provides a direction of investigation to
derive approximation for functionals with discontinuities penalized with a
"cohesive" energy, that is, whose cost depends on the actual opening of the
discontinuity
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