Related papers: Hypoelliptic Estimates for a Linear Model of the B…

We consider Fokker--Planck--Kolmogorov equations with unbounded coefficients and obtain upper estimates of solutions. We also obtain new estimates involving Lyapunov functions.

We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of characteristics or on…

We derive an a priori real Hessian estimate for solutions of a large family of geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent of a lower bound for the right-hand side function. This…

In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.

In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We…

Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…

We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary…

We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to…

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…

We prove the existence of non-smooth solutions to fully nonlinear uniformly elliptic equations.

This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…

In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat…

This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…

In this paper, we extend the nontangential maximal function estimate obtained by C. Kenig, F. Lin and Z. Shen in \cite{KFS1} to the nonhomogeneous elliptic operators with rapidly oscillating periodic coefficients. The result relies on the…

This paper investigates the well-posedness of the inhomogeneous Boltzmann and Landau equations in critical function spaces, a fundamental open problem in kinetic theory. We develop a new analytical framework to establish local…

We study fully nonlinear parabolic equations in nondivergence form with oblique boundary conditions. An optimal and global Calder\'{o}n-Zygmund estimate is obtained by proving that the Hessian of the viscosity solution to the oblique…

We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted $L^p$-Norm. The estimate holds for a wide range of potentials including soft potentials as well as very soft potentials. As an…

Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…