Related papers: Free boundary on a cone
We report results from Monte Carlo simulations of a thin film superconductor in a spherical geometry within the lowest Landau level approximation. We observe the absence of a phase transition to a low temperature vortex solid phase with…
In this paper we study a mass-constrained free boundary problem modeling cell polarization, in the regime where the mass is small. In the generic case of a signal with nondegenerate maxima, we prove that the solution converges locally to a…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
Given a Riemannian manifold and a closed submanifold, we find a geodesic segment with free boundary on the given submanifold. This is a corollary of the min-max theory which we develop in this article for the free boundary variational…
A free boundary problem arising from materials science is studied in one-dimensional case. The problem studied here is an obstacle problem for the non-convex energy consisting of a bending energy, tension and an adhesion energy. If the…
We consider smooth bounded surfaces with a smooth boundary and a prescribed background metric g_0. We now consider all metrics g conformal to g_0 which have a prescribed volume M. We now minimize the first eigenvalue of the Laplace operator…
We investigate the persistence of spectral gaps of one-dimensional frustration free quantum lattice systems under weak perturbations and with open boundary conditions. Assuming the interactions of the system satisfy a form of local…
For the problem describing steady, gravity waves with vorticity on a two-dimensional, unidirectional flow of finite depth the following results are obtained. (i) Bounds for the free-surface profile and for Bernoulli's constant. (ii) If only…
We construct non-flat minimal capillary cones with bi-orthogonal symmetry groups for any dimension and contact angle. These cones interpolate between rescalings of a singular solution to the one-phase problem and the free-boundary cone…
We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains $\Omega \subset \mathbb{R}^n$. For a rotationally invariant Cheeger set $C$, the free boundary $\partial C \cap \Omega$ consists of pieces of…
In [20], Ros and Vergasta proved that an immersed orientable compact stable constant mean curvature surface $\Sigma$ with free boundary in a closed ball $B\subset\mathbb{R}^3$ must be a planar equator, a spherical cap or a surface of genus…
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free edges have remained elusive. Intuitively, unstretchability…
We study the existence and multiplicity of solutions of the following free boundary problem $$ (P)\left\{ \begin{array}{rcll} \del u &=& \lam ( \eps +(1-\eps ) H(u-\mu))~ \hspace{3mm}&\text{in}~\Omega (t)\\ u&=&…
The gonality of a smooth geometrically connected curve over a field $k$ is the smallest degree of a nonconstant $k$-morphism from the curve to the projective line. In general, the gonality of a curve of genus $g \ge 2$ is at most $2g - 2$.…
In this paper we investigate free boundary minimal surfaces in the unit ball in Euclidean 3-space, and by using holomorphic techniques we prove that intersection curves of free boundary minimal surfaces with the unit sphere are all circles.
Motivated by the study of the non-parametric area $\mathcal A$ of the graph of the vortex map $u$ (a two-codimensional singular surface in $\mathbb R^4$) over the disc $\Omega \subset \mathbb R^2$ of radius $l$, we perform a careful…
In this paper, we study almost minimizers to a fractional Alt-Caffarelli-Friedman type functional. Our main results concern the optimal $C^{0,s}$ regularity of almost minimizers as well as the structure of the free boundary. We first prove…