相关论文: Low frequency resolvent estimates for long range p…

We prove optimal high-frequency resolvent estimates for perturbations by large magnetic and electric potentials

We study local in time Strichartz estimates for the Schroedinger equation associated to long range perturbations of the flat Laplacian on the euclidean space. We prove that in such a geometric situation, outside of a large ball centered at…

We establish global bounds for solutions to stationary and time-dependent Schr\"odinger equations associated with the sublaplacian $\mathcal L$ on the Heisenberg group, as well as its pure fractional power $\mathcal L^s$ and conformally…

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $$u_t=\Delta_\phi(u^p)$$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the…

I offer a simple and useful formula for the resolvent of a small rank perturbation of large matrices. I discuss applications of this formula, in particular, to analytical and numerical solving of difference boundary value problems. I…

In this work, we explore a numerical approach for performing the inverse Laplace transformation, with an emphasis on achieving stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data…

We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.

We study the perturbation of bound states embedded in the continuous spectrum which are unstable by the Fermi Golden Rule. The approach to resonance theory based on spectral deformation is extended to a more general class of quantum systems…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

We explore the connection between $k$-broad Fourier restriction estimates and sharp regularity $L^p-L^q$ local smoothing estimates for the solutions of the wave equation in $\mathbb{R}^{n}\times \mathbb{R}$ for all $n \geq 3$ via a…

Small perturbation of the Liouville equation under smooth initial data is considered. Asymptotic solution which is available for a long time interval is constructed by the two scale method.

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away…

We present a simple proof of the resolvent estimates of elliptic Fourier multipliers on the Euclidean space, and apply them to the analysis of time-global and spatially-local smoothing estimates of a class of dispersive equations. For this…

In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or…

In this paper, we obtain gradient estimates and Laplacian estimates for the solution to the singular complex Monge-Amp\`ere equation by applying the integral method.

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric assumptions on the obstacle there exists an algorithm whose…

We study in this paper the continuous and discrete Euler-Lagrange equations arising from a quadratic lagrangian. Those equations may be thought as numerical schemes and may be solved through a matrix based framework. When the lagrangian is…

The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…