Related papers: Higher integrability and approximation of minimal …
Analytic continuations of integer-valued parameters can lead to profound insights, such as angular momentum in Regge theory, the number of replicas in spin glasses, the number of internal degrees of freedom, the spacetime dimension in…
We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set, namely $$ \int_\Om |\nabla u(x)|^2\,dx+\Per\Big(\{u > 0\},\Om \Big),$$ with $\sigma\in(0,1)$. We obtain regularity results for…
After defining a notion of $\epsilon$-density, we provide for any real algebraic number $\alpha$ an estimate of the smallest $\epsilon$ such that for each $m>1$ the set of vectors of the form $(t,t\alpha,...,t\alpha^{m-1})$ for $t\in\R$ is…
We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient and which is related to the minimization of the nonlocal…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
We provide new elementary proofs of the following two results: every complex variety is locally the graphs of a Dir-minimizing function, first proved by Almgren; the gradients of Dir-minimizing functions, in principle square-summable, are…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…
Solutions to elliptic equations often exhibit higher regularity properties such as \emph{higher integrability}. That is, for instance, a solution $u$ to a system that a priori only satisfies $ u \in W^{1,r}$ is more regular and even in the…
We show local higher integrability of derivative of a suitable weak solution to the surface growth model, provided a scale-invariant quantity is locally bounded. If additionally our scale-invariant quantity is small, we prove local…
We show a higher order integrability theorem for distributions generated by a family of vector fields under a horizontal regularity assumption on their coefficients. We use as chart a class of almost exponential maps which we discuss in…
We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The…
We provide new general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. A new direct proof of Almgren's 1968 existence result is presented; namely, we produce from a class of…
We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the…
Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…
We contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free lattice fermions in…
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating…
In this paper, we systematically study the regularity theory of the linear system of nearly incompressible elasticity. In the setting of stochastic homogenization, we develop new techniques to establish the large-scale estimates of…
Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function, identifying the respective most linear region of operation with a fixed width. This…
The central quantity of density functional theory is the so-called exchange-correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of…