Related papers: Multi-Bubble Isoperimetric Problems
For any closed Riemannian manifold $X$ we prove that large isoperimetric regions in $X\times{\mathbb R}^n$ are of the form $X\times$(Euclidean ball). We prove that if $X$ has non-negative Ricci curvature then the only soap bubbles enclosing…
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…
Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. They can…
The multi-bubble isoperimetric conjecture in $n$-dimensional Euclidean and spherical spaces from the 1990's asserts that standard bubbles uniquely minimize total perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q \leq…
We study the double bubble problem with perimeter taken with respect to the $\ell_1$ norm on $\mathbb{R}^2$. We give an elementary proof for the existence of minimizing sets for any volume ratio parameter $0<\alpha\le1$ by direct comparison…
We establish a generic weak uniqueness result and partial regularity of the free boundary and of minimizers for the composite membrane problem.
The paper addresses the existence of multi-bubble solutions for the well-known Brezis-Nirenberg problem. Although there is extensive literature on the subject, the existence of solutions that blow up at multiple points in a 4D bounded…
We carry out a series of experiments with a special interest on growing and condensing processes of vapor bubble(s) injected into a subcooled pool. We examine effects of the degree of subcooling of the bulk in the pool and injection rate of…
This letter describes a periodically oscillating microfoam flow. For constant input parameters, both the produced bubble volume and the flow rate vary over a factor two. We explicit the link between foam topology alternance and flow rate…
Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super…
Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens…
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and…
We study the dynamics of a cosmological bubble wall beyond the approximation of an infinitely thin wall. In a previous paper, we discussed the range of validity of this approximation and estimated the first-order corrections due to the…
Soap bubbles can be easily generated by varies methods, while their formation process is complicated and still worth study. A model about the bubble formation process was proposed in Phys. Rev. Lett. 116, 077801 recently, and it was…
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
In this work we derive a class of geometric flow equations for metric-scalar systems. Thereafter, we construct them from some general string frame action by performing volume-preserving fields variations and writing down the associated…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
This paper is concerned with volume-constrained minimization problems derived from Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter term and repulsive nonlocal potentials. We consider a large class…
The main problem in liquid porosimetry, which prevents to see the pore sizes smaller than 2 microns in diameter, is direct gas diffusion flow through a micro-porous membrane. This diffusion causes bubbles formation below the membrane and…