Related papers: Maximal estimates for orthonormal systems of wave …
Let $\mathscr{H}^2$ denote the Hardy space of Dirichlet series $f(s) = \sum_{n\geq1} a_n n^{-s}$ with square summable coefficients and suppose that $\varphi$ is a symbol generating a composition operator on $\mathscr{H}^2$ by…
This paper is devoted to studying the maximal-in-time estimates and Strichartz estimates for orthonormal functions and convergence problem of density functions related to Boussinesq operator on manifolds. Firstly, we present the pointwise…
In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates…
This paper is concerned with the large time behavior of the solution to the Cauchy problem for the elastic wave equations. In particular, optimal $L^{2}$ estimates of the elastic waves are obtained in the sense that the upper and lower…
We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and…
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schr\"odinger equations. Our results generalize the classical (single-function) Strichartz…
This paper is concerned with the quantitative homogenization of $2m$-order elliptic systems with bounded measurable, rapidly oscillating periodic coefficients. We establish the sharp $O(\varepsilon)$ convergence rate in $W^{m-1, p_0}$ with…
Schultz \cite{S98} proved dispersive estimates for the wave equation on lattice graphs $\mathbb{Z}^d$ for $d=2,3,$ which was extended to $d=4$ in \cite{BCH23}. By Newton polyhedra and the algorithm introduced by Karpushkin \cite{K83}, we…
We give several remarks on Strichartz estimates for homogeneous wave equation with special attention to the cases of $L^\infty_x$ estimates, radial solutions and initial data from the inhomogeneous Sobolev spaces. In particular, we give the…
We derive a robust error estimate for a recently proposed numerical method for $\alpha$-dissipative solutions of the Hunter-Saxton equation, where $\alpha \in [0, 1]$. In particular, if the following two conditions hold: i) there exist a…
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1,…
We establish new results concerning the existence of extremisers for a broad class of smoothing estimates of the form $\|\psi(|\nabla|) \exp(it\phi(|\nabla|)f \|_{L^2(w)} \leq C\|f\|_{L^2}$, where the weight $w$ is radial and depends only…
In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schr\"odinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the…
We prove optimal dispersive estimates at high frequency for the Schrodinger group with real-valued potentials $V(x)=O(|x|^{-\delta})$, $\delta>n-1$, and $V\in C^k({\bf R}^n$, $k>k_n$, where $n\ge 4$ and $(n-3)/2\le k_n<n/2$. We also give a…
We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for…
In this paper, we establish sharp dispersive estimates for the linear wave equation on the lattice $\mathbb{Z}^d$ with dimension $d=4$. Combining the singularity theory with results in uniform estimates of oscillatory integrals, we prove…
We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as…
In this paper, we establish explicit convergence rates for the stochastic smooth approximations of infimal convolutions introduced and developed in \cite{MR4581306,MR4923371}. In particular, we quantify the convergence of the associated…
It is well known that under general regularity conditions the distribution of the maximum likelihood estimator (MLE) is asymptotically normal. Very recently, bounds of the optimal order $O(1/\sqrt n)$ on the closeness of the distribution of…
We prove optimal convergence rates for certain low-regularity integrators applied to the one-dimensional periodic nonlinear Schr\"odinger and wave equations under the assumption of $H^1$ solutions. For the Schr\"odinger equation we analyze…