Related papers: Lower semicontinuity for functionals defined on pi…
The ab initio simulation of charged interfaces in the framework of density functional theory (DFT) is heavily employed for the study of electrochemical energy conversion processes. The capacitance is the primary descriptor for the response…
This paper is devoted to the asymptotic analysis of a fractional version of the Ginzburg-Landau equation in bounded domains, where the Laplacian is replaced by an integro-differential operator related to the square root Laplacian as defined…
We consider second order phase field functionals, in the continuum setting, and their discretization with isogeometric tensor product B-splines. We prove that these functionals, continuum and discrete, $\Gamma$-converge to a brittle…
This work concerns stationary Stokes type systems governed by a general class of non-necessarily power-type nonlinearities. Fractional regularity properties of the symmetric gradient of local solutions are established, depending on a…
We introduce the new space $BV^{\alpha}(\mathbb{R}^n)$ of functions with bounded fractional variation in $\mathbb{R}^n$ of order $\alpha \in (0, 1)$ via a new distributional approach exploiting suitable notions of fractional gradient and…
In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
Given an elliptic differential operator L of second order with smooth coefficients in a bounded domain with smooth boundary. We show that if the coefficients are H\"older-continuous up to the boundary and the boundary is…
A new yield/damage function is proposed for modelling the inelastic behaviour of a broad class of pressure-sensitive, frictional, ductile and brittle-cohesive materials. The yield function allows the possibility of describing a transition…
This work considers an Inertial version of Bregman Proximal Gradient algorithm (IBPG) for minimizing the sum of two single-valued functions in finite dimension. We suppose that one of the functions is proper, closed, and convex but…
We investigate the effect of a dynamical collective mode coupled with quasiparticles at specific wavevectors only. This coupling describes the incipient tendency to order and produces shadow spectral features at high energies, while leaving…
We consider the Dirichlet problem for second-order elliptic systems with constant coefficients. We prove that non-reducible strongly elliptic systems of this type do not admits non-negatively defined energy functionals of the form…
In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$ where the parameter $0 <\beta\leq 1$ and the equation of an electrical network…
We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex…
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…
The Cabibbo-suppressed semileptonic decay $B^{+}\to p\overline{p}\mu^{+}\nu_{\mu}$ is observed for the first time using a sample of $pp$ collisions corresponding to an integrated luminosity of 1.0, 2.0 and 1.7fb$^{-1}$ at centre-of-mass…
The purpose of this paper is to study the existence of solutions for semilinear elliptic system driven by fractional Laplacian and establish some new existence results which are obtained by virtue of the local linking theorem and the saddle…
We consider gradient descent equations for energy functionals of the type S(u) = 1/2 < u(x), A(x)u(x) >_{L^2} + \int_{\Omega} V(x,u) dx, where A is a uniformly elliptic operator of order 2, with smooth coefficients. The gradient descent…
In this paper, we give a full classification of the nonexistence of positive weak solutions to the semilinear elliptic inequality involving the fractional Hardy potential in punctured and in exterior domains. Our methods are self-contained…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…