Related papers: Minimum Riesz energy problems for a condenser with…
Conventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
We consider the minimal discrete and continuous energy problems on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field due to finitely many localized charge distributions on…
A number of boundary problems in multidimensional elasticity theory are solved. The solutions can be treated as the simplest cosmological models. Some specific properties of the solutions and experimental consequences of the theory are…
Building on work of Mondino-Scharrer, we show that among closed, smoothly embedded surfaces in $\mathbb{R}^3$ of genus $g$ and given isoperimetric ratio $v$, there exists one with minimum bending energy $\mathcal{W}$. We do this by gluing…
Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We study the Cauchy problem for nonlinear Schr\"odinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of global well-posedness and blow-up for the equation in the…
We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization and investigate the role of global minimizers among graph…
Thomson's theorem states that static charge distributions in conductors only exist at the conducting surfaces in an equipotential configuration, yielding a minimal electrostatic energy. In this work we present a proof for this theorem based…
We consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the $x$-axis. First, we show the existence of ground states as minimizers of the action or of the energy under suitable…
In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that…
We study the effective elastic behavior of incompatibly prestrained plates, where the prestrain is independent of thickness as well as uniform through the thickness. We model such plates as three-dimensional elastic bodies with a prescribed…
In harmonic analysis, the studies of inequalities of classical operators (= singular, maximal, Riesz potentials etc.) in various function spaces have a very important place. The maturation of many topics in the field of harmonic analysis,…
Energy minimality selects among possible configurations of a continuous body with and without cracks those compatible with assigned boundary conditions of Dirichlet-type. Crack paths are described in terms of curvature varifolds so that we…
We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface…
In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system $$ \begin{cases} -\Delta u_i + \lambda_i u_i = \mu_i|u_i|^{Kq-2}u_i + \beta|u_i|^{q-2}u_i\prod_{j\neq i}|u_j|^q & \text{in…
In the nonlocal Almgren problem, the goal is to investigate the convexity of a minimizer under a mass constraint via a nonlocal free energy generated with some nonlocal perimeter and convex potential. In the paper, the main result is a…
We study periodic tessellations of the Euclidean space with unequal cells arising from the minimization of perimeter functionals. Existence results and qualitative properties of minimizers are discussed for different classes of problems,…
The purpose of this work is twofold. First, we aim to extend for $0<s<1$ the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials…