A Liouville theorem for minimizers with finite potential energy for the vectorial Allen-Cahn equation

We prove that if a globally minimizing solution to the vectorial Allen-Cahn equation has finite potential energy, then it is a constant

On the confinement of bounded entire solutions to a class of semilinear elliptic systems

Under appropriate assumptions, we show that all bounded entire solutions to a class of semilinear elliptic systems are confined in a convex domain. Moreover, we prove a Liouville type theorem in the case where the domain is strictly convex. Our result represents an extension, under less regularity assumptions, of a recent result. We also provide several application

Evaluation of WRF performance for the analysis of surface wind speeds over various Greek regions

In this study we analyze the surface wind variability over selected areas of the Greek territory by comparing a 3-Km spatial resolution simulation performed with the Weather Research and Forecasting (WRF) model for the summer months of 2013 with actual surface measurements. Daily 36hrs runs at 12 UTC were driven by FLN (1 deg x 1 deg) data for the period of 11 July 2013 to 17 July 2013. Various verification statistics such as BIAS, RMSE and DACC for wind speed and direction were used to gauge the mesoscale model performance

Asymptotic Solutions of the Phase Space Schrodinger Equation: Anisotropic Gaussian Approximation

We consider the singular semiclassical initial value problem for the phase space Schrodinger equation. We approximate semiclassical quantum evolution in phase space by analyzing initial states as superpositions of Gaussian wave packets and applying individually semiclassical anisotropic Gaussian wave packet dynamics, which is based on the the nearby orbit approximation; we accordingly construct a semiclassical approximation of the phase space propagator, semiclassical wave packet propagator, which admits WKBM semiclassical states as initial data. By the semiclassical propagator we construct asymptotic solutions of the phase space Schrodinger equation, noting the connection of this construction to the initial value repsresentations for the Schrodinger equation

Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation

We prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result in all dimensions

A weighted Hardy-Sobolev-Maz’ya inequality

We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and Tertikas

On the XFEL Schroedinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

We analyse a nonlinear Schr\"odinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree-Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray Free Electron Laser (XFEL). We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schr\"odinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential

The heteroclinic connection problem for general double-well potentials

By variational methods, we provide a simple proof of existence of a heteroclinic orbit to a second order Hamiltonian ODE that connects the two global minima of a double-well potential. Moreover, we consider several inhomogeneous extensions

Regularity of weak solutions to rate-independent systems in one-dimension

We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate-independent system is of class SBV, or has fi�nite jumps, or is even piecewise C1. Our assumption is essentially imposed on the energy functional, but not convexity is required