Related papers: Localization principle and relaxation
Rotational invariance of physical laws is a generally accepted principle. We show that it leads to an additional external constraint on local realistic models of physical phenomena involving measurements of multiparticle spin 1/2…
We derive a global higher regularity result for weak solutions of the linear relaxed micromorphic model on smooth domains. The governing equations consist of a linear elliptic system of partial differential equations that is coupled with a…
We consider periodic homogenization of nonlinearly elastic composite materials. Under suitable assumptions on the stored energy function (frame indifference; minimality, non-degeneracy and smoothness at identity; $p\geq d$-growth from…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
In this paper we present a new proof of the sufficiency theorem for strong local minimizers concerning $C^1$-extremals at which the second variation is strictly positive. The results are presented in the quasiconvex setting, in accordance…
Many-body localization (MBL) is understood theoretically through the existence of an extensive number of local integrals of motion (LIOMs). These conserved quantities are related to the microscopic quantum degrees of freedom that are…
In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight $w$. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting…
We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form \[ \mathcal{F}[u] := \int_{\Omega} f \bigg( \frac{1}{2} \bigl( \nabla u(x) + \nabla u(x)^T \bigr) \bigg)\,\mathrm{d} x, \qquad u : \Omega…
We consider the functional \[ F(u)=\int_{\Omega} f(\nabla u)\,dx\qquad u\in\varphi+W^{1,1}_0(\Omega) \] where $\Omega$ is a Lipschitz bounded open set of $\R^N$, $f:\R^N\to\R\cup \{+\infty\}$ is a superlinear Borel function, $\varphi\in…
We prove a moment majorization principle for matrix-valued functions with domain $\{-1,1\}^{m}$, $m\in\mathbb{N}$. The principle is an inequality between higher-order moments of a non-commutative multilinear polynomial with different random…
We consider vectorial variational problems in nonlinear elasticity of the form $I[u]=\int W(Du)dx$, where $W$ is continuous on matrices with positive determinant and diverges to infinity long sequences of matrices whose determinant is…
Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the…
Here we develop a regularity theory for a polyconvex functional in $2\times2-$dimensional compressible finite elasticity. In particular, we consider energy minimizers/stationary points of the functional…
We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…
We study quantum oscillator lattice systems with disorder, in arbitrary dimension, requiring only partial localization of the associated effective one-particle Hamiltonian. This leads to a many-body localized regime of excited states with…
We prove the existence of minimizers of causal variational principles on second countable, locally compact Hausdorff spaces. Moreover, the corresponding Euler-Lagrange equations are derived. The method is to first prove the existence of…
Recently a generalization of the ``\textit{modern theory of orbital magnetization}'' to include non-local Hamiltonians (e.g. hybrid functionals of the generalized Kohn-Sham theory) was provided for magnetic response properties. Results…
This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of $p$-Laplacian type with absorption and (prescribed) locally integrable forcing posed in…
Many-body localisation in disordered systems in one spatial dimension is typically understood in terms of the existence of an extensive number of (quasi)-local integrals of motion (LIOMs) which are thought to decay exponentially with…
For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a…