Related papers: W^{1,1}_0 minima of non coercive functionals
Minima of functionals of the type $$ w\mapsto \int_{\Omega}\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, \alpha}\,,$$ with $\Omega \subset \er^n$, have locally H\"older continuous gradient…
The purpose of this paper is to consider the minimization problem of the following nonlocal interaction functional \begin{equation*} E[\rho]=\frac{1}{2}\int_{\mathbb{R}^N}…
We consider minimization problems of functionals given by the difference between the Willmore functional of a closed surface and its area, when the latter is multiplied by a positive constant weight $\Lambda$ and when the surfaces are…
We first show a counter intuitive result that in the ring of real valued continuous functions on $[0,1]$ non maximal prime ideals exist. This is a standard proof and a well known result. Interestingly, a non maximal prime ideal in this ring…
We study stochastic homogenization for convex integral functionals $$u\mapsto \int_D W(\omega,\tfrac{x}\varepsilon,\nabla u)\,\mathrm{d}x,\quad\mbox{where}\quad u:D\subset \mathbb{R}^d\to\mathbb{R}^m,$$ defined on Sobolev spaces. Assuming…
In this paper we prove symmetry results for minimizers of a non coercive functional defined on the class of Sobolev functions with zero mean value. We prove that the minimizers are foliated Schwarz symmetric, i.e. they are axially symmetric…
We consider the generalized Wirtinger inequality \[ (\int_{0}^{T} a |u|^q )^{1/q} \le C \biggm(\int_{0}^{T} a^{1-p} |u'|^{p}\biggm)^{1/p}, \] with $p,q>1$, $T>0$, $a\in L^1[0,T]$, $a\ge0$, $a\not\equiv0$ and where $u$ is a $T$-periodic…
We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation}…
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…
It is known that an elliptic system $\{P_j(x,D)\}_1^N$ of order $l$ is weakly coercive in $\overset{\circ}{W}\rule{0pt}{2mm}^l_\infty(\mathbb R^n)$, that is, all differential monomials of order $\le l-1$ on $C_0^\infty(\mathbb…
We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic…
The aim of the present paper is essentially to prove that if $\Phi$ and $\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\Psi$ is also continuous and coercive, then then following…
This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \newa{of Boolean functions} and high-dimensional geometry. \begin{enumerate} \item It has been known since 1994 \cite{GL:94} that…
We present a generalization of a technical lemma due to Boccardo and Orsina, and then give an application to regularity of minima for integral functionals noncoercive in the energy space.
We provide a general condition on the kernel of an integro-differential operator so that its associated quadratic form satisfies a coercivity estimate with respect to the $H^s$-seminorm.
We discuss the $\Gamma$-convergence, under the appropriate scaling, of the energy functional $$ \|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)dx,$$ with $s \in (0,1)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the…
In this article, we present weighted norm inequality for a fractional one-sided minimal function. We prove weighted weak and strong type norm inequalities for the one-sided minimal function on $\mathbb{R}.$ We construct two weight classes…
In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…
We prove a sharp higher differentiability result for local minimizers of functionals of the form $$\mathcal{F}\left(w,\Omega\right)=\int_{\Omega}\left[ F\left(x,Dw(x)\right)-f(x)\cdot w(x)\right]dx$$ with non-autonomous integrand $F(x,\xi)$…
We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.