ﻻ يوجد ملخص باللغة العربية
We consider wave equations with time-independent coefficients that have $C^{1,1}$ regularity in space. We show that, for nontrivial ranges of $p$ and $s$, the standard inhomogeneous initial value problem for the wave equation is well posed in Sobolev spaces $mathcal{H}^{s,p}_{FIO}(mathbb{R}^{n})$ over the Hardy spaces $mathcal{H}^{p}_{FIO}(mathbb{R}^{n})$ for Fourier integral operators introduced recently by the authors and Portal, following work of Smith. In spatial dimensions $n = 2$ and $n=3$, this includes the full range $1 < p < infty$. As a corollary, we obtain the optimal fixed-time $L^{p}$ regularity for such equations, generalizing work of Seeger, Sogge and Stein in the case of smooth coefficients.
Multifractal analysis aims to characterize signals, functions, images or fields, via the fluctuations of their local regularity along time or space, hence capturing crucial features of their temporal/spatial dynamics. Multifractal analysis is becomin
This article addresses the local boundedness and Holder continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and transport. Al
In this paper, we study parabolic equations in divergence form with coefficients that are singular degenerate as some Muckenhoupt weight functions in one spatial variable. Under certain conditions, weighted reverse H{o}lders inequalities are establis
We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m) with p in (1,infty). Sufficient conditions to prove generation results of an analytic C_0-semigroup
The Hardy spaces for Fourier integral operators $mathcal{H}_{FIO}^{p}(mathbb{R}^{n})$, for $1leq pleq infty$, were introduced by Smith in cite{Smith98a} and Hassell et al. in cite{HaPoRo18}. In this article, we give several equivalent characterizatio