Related papers: Donoho-Logan large sieve principles for the wavele…
We build on the recent techniques of Codogni and Patakfalvi, from \cite{Codogni:Patakfalvi:2021}, which were used to establish theorems about semi-positivity of the Chow Mumford line bundles for families of $\K$-semistable Fano varieties.…
Let $p(\cdot):\ \mathbb R^n\to(0,1]$ be a variable exponent function satisfying the globally log-H\"older continuous condition and $L$ a one to one operator of type $\omega$ in $L^2({\mathbb R}^n)$, with $\omega\in[0,\,\pi/2)$, which has a…
We define local Hardy spaces of differential forms $h^p_{\mathcal D}(\wedge T^*M)$ for all $p\in[1,\infty]$ that are adapted to a class of first order differential operators $\mathcal D$ on a complete Riemannian manifold $M$ with at most…
We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main…
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…
In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes.…
For the wavelet type orthonormal systems $\phi_n$, we establish a new bound \begin{equation} \left\|\max_{1\le m\le n}\left|\sum_{j\in G_m}\langle f,\phi_j\rangle \phi_j\right|\right\|_p\lesssim \sqrt{\log (n+1)}\cdot \|f\|_p,\quad…
Given a measure $\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\mathrm{supp}(\mu)$ which provides the right framework for a dyadic form of nondoubling harmonic…
Let $\phi: \mathbb{R}^n\times[0,\fz)\rightarrow[0,\fz)$ be a function such that $\phi(x,\cdot)$ is an Orlicz function and $\phi(\cdot,t)\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$ (the class of local weights introduced by V. S.…
In this paper, we address the question of the hyperbolicity and the local well- posedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of…
In this paper, we provide sufficient conditions for the functions $\psi$ and $\phi$ to be the approximate duals in the Hardy space $H^p(\mathbb{R})$ for all $0<p\leq1$. Based on these conditions, we obtain the wavelet series expansion in…
The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi resolution analysis properties. These relatively new representation systems have encountered wide range…
We use the dispersive properties of the linear Schr\"{o}dinger equation to prove local well-posedness results for the Boltzmann equation and the related Boltzmann hierarchy, set in the spatial domain $\mathbb{R}^d$ for $d\geq 2$. The proofs…
In this paper, we study the localization phenomena in a slender cylinder composed of an incompressible hyperelastic material subjected to axial tension. We aim to construct the analytical solutions based on a three-dimensional setting and…
The paper is concerned with the sparse approximation of functions having hybrid regularity borrowed from the theory of solutions to electronic Schr\"odinger equations due to Yserentant [43]. We use hyperbolic wavelets to introduce…
Optimal linear feedback control design is a valuable but challenging problem due to nonconvexity of the underlying optimization and infinite dimensionality of the Hardy space of stabilizing controllers. A powerful class of techniques for…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
We study hypercontractivity for the underdamped Langevin dynamics with a convex confining potential. Unlike in the overdamped case, the noise acts only on the velocity variable, so the usual argument based on the logarithmic Sobolev…