Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity
Inégalité isopérimétrique en dimension 3 d'après B. Kleiner
Influence of a boundary perforation on the Dirichlet energy
Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation
In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo...
Inverse shape optimization problems and application to airfoils
Isoperimetric and Stable Sets for Log-Concave Perturbations of Gaussian Measures
Let be an open half-space or slab in ℝn+1 endowed with a perturbation of the Gaussian measure of the form f (p) := exp(ω(p) − c|p|2), where c > 0 and ω is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to ∂ Ω. In this work we follow a variational approach to show that half-spaces perpendicular to ∂ Ω uniquely minimize the weighted perimeter in Ω among sets enclosing the same weighted volume. The main ingredient of the proof is the characterization...
Isoperimetric Regions in Rnwith Density rp
We show that the unique isoperimetric regions in Rn with density rp for n ≥ 3 and p > 0 are balls with boundary through the origin.
Isoperimetric regions in the plane with density .
Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture
We give an example of a smooth surface of revolution for which all circles about the origin are strictly stable for fixed area but small isoperimetric regions are nearly round discs away from the origin.