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 Γ\Gamma-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 $\Gamma$-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