Related papers: Partial regularity for minimizers of singular ener…
We discover a new minimality property of the absolute minimisers of supremal functionals (also known as $L^\infty$ Calculus of Variations problems).
We consider regularity for solutions of a class of de Rham's functional equations. Under some smoothness conditions of functions consisting the equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our results are…
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a…
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
In this paper we study nonnegative minimizers of general degenerate elliptic functionals, $\int F(X,u,Du) dX \to \min$, for variational kernels $F$ that are discontinuous in $u$ with discontinuity of order $\sim \chi_{\{u > 0 \}}$. The…
We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of $(p,q)$-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness…
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded,…
We will study an open problem pertaining to the uniqueness of minimizers for a class of variational problems emanating from Meyer's model for the decomposition of an image into a geometric part and a texture part. Mainly, we are interested…
We analyze an elastic surface energy which was recently introduced by G. Napoli and L.Vergori to model thin films of nematic liquid crystals. We show how a novel approach that takes into account also the extrinsic properties of the surfaces…
We study almost-minimizers of anisotropic surface energies defined by a H\"older continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers…
We investigate regularity of minimizers in two dimensions for certain classes of non-smooth convex functionals. In particular our results apply to the surface tensions that appear in recent works on random surfaces and random tilings of…
In our previous work,, we studied asymptotic behavior of minimizers of the Landau-de Gennes energy functional on planar domains as the nematic correlation length converges to zero. Here we improve upon those results, in particular by…
A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending…
In this survey article we revisit Hilbert's $19^{\text{th}}$ problem concerning the regularity of minimizers of variational integrals. We first discuss the classical theory (that is, the statement and resolution of Hilbert's problem in all…
We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.
We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any…
We study global minimizers of the Landau-de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary…
We investigate the vanishing elasticity limit for minimizers of the Landau-de Gennes model with finite energy. By adopting a refined blow-up and covering analysis, we establish the optimal $ L^p $ ($ 1<p<+\infty $) convergence of minimizers…
In this paper, we extend the related notions of Dirichlet quasiminimizer, $\omega-$minimizer and almost minimizer to the framework of multiple-valued functions in the sense of Almgren and prove Holder regularity results. We also give…