Related papers: Displacement convexity and minimal fronts at phase…
We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
We establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line. The class of equations includes most importantly nonlinear…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
It is well known that a strictly convex minimand admits at most one minimizer. We prove a partial converse: Let $X$ be a locally convex Hausdorff space and $f \colon X \mapsto \left( - \infty , \infty \right]$ a function with compact…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
For any $M, n \geq 2$ and any open set $\Omega \subset \mathbb{R}^n$ we find a smooth, strongly polyconvex function $F\colon \mathbb{R}^{M\times n}\to \mathbb{R}$ and a Lipschitz map $u\colon \mathbb{R}^n \to \mathbb{R}^M$ that is a weak…
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…
Some mathematical inconsistencies in the conventional form of Maxwell's equations extended by Lorentz for a single charge system are discussed. To surmount these in framework of Maxwellian theory, a novel convection displacement current is…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
In this paper we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider the displacement problem in which the…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
We present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes…
We study equilibria in domains with boundaries for a first-order aggregation model that includes social interactions and exogenous forces. Such equilibrium solutions can be connected or disconnected, the latter consisting in a delta…
It is shown that a possibly infinite-valued proper lower semicontinuous convex function on ${\mathbb R}^n$ has an extension to a convex function on the half-space ${\mathbb R}^n\times[0,\infty)$ which is finite and smooth on the open…
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of…