Related papers: Maximizers for Strichartz Inequalities on the Toru…
We study synchronization in scalar nonlinear systems connected over a linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network systems expressed in terms of…
In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer \cite{FLLS} and Frank-Sabin \cite{frank-sabin-1}, we study the Strichartz inequality on torus with the orthonormal system input and obtain sharp estimates…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of…
Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire…
We consider an optimal rearrangement maximization problem involving the fractional Laplace operator $(-\Delta)^s$, $0<s<1$, and the Gagliardo-Nirenberg seminorm $[u]_s$. We prove the existence of a maximizer, analyze its properties and show…
A theorem of Strichartz states that if a uniformly bounded bi-infinite sequence of functions on the Euclidean spaces, satisfies the condition that the Laplacian acting on a function in this sequence yields the next one, then each function…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
We study the standing waves for a fourth-order Schr\"odinger equation with mixed dispersion that minimize the associated energy when the $L^2-$norm (the \textit{mass}) } is kept fixed. We need some non-homogeneous Gagliardo-Nirenberg-type…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the…
In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…
We study the dispersive properties of the linear Schr\"odinger equation with a time-dependent potential $V(t,x)$. We show that an appropriate integrability condition in space and time on $V$, i.e. the boundedness of a suitable…
Given a finite sequence of vectors $\mathcal F_0$ in $\C^d$ we characterize in a complete and explicit way the optimal completions of $\mathcal F_0$ obtained by adding a finite sequence of vectors with prescribed norms, where optimality is…
In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the maximizers, hence obtain a family of stable traveling vortex…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…