Related papers: Sharp $L^1$ estimates for singular transport equat…

This paper is concerned with Schr\"odinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate,…

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These…

An $\left( n+1\right) -$D coefficient inverse problem for the radiative stationary transport equation is considered for the first time. A globally convergent so-called convexification numerical \ method is developed and its convergence…

We consider the 1D transport equation with nonlocal velocity field: \begin{equation*}\label{intro eq} \begin{split} &\theta_t+u\theta_x+\nu \Lambda^{\gamma}\theta=0, \\ & u=\mathcal{N}(\theta), \end{split} \end{equation*} where…

We introduce a new condition on elliptic operators $L= {1/2}\triangle + b \cdot \nabla $ which ensures the validity of the Liouville property for bounded solutions to $Lu=0$ on $\R^d$. Such condition is sharp when $d=1$. We extend our…

We show how to compute transport coefficients in gauge theories by considering the expansion of the Kubo formulas in terms of ladder diagrams in the imaginary time formalism. All summations over Matsubara frequencies are performed and the…

We establish some weighted $L^2$ estimates for the Fourier extension operator in $\mathbb{R}^2$ and discuss several applications to $L^p$ problems. These include estimates for the maximal Schr\"odinger operator and the maximal extension…

Sharp estimates of solutions of the classical heat equation are proved in $L^p$ norms on the real line.

We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

We propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special type. We propose some kind of "algebra" on different models and corresponding…

Spectrum of a certain class of first order conformally invariant operators on the sphere is explicitly computed. The class contains the (elliptic verions of) Rarita-Schwinger operator and its higher spin analogues.

We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully…

We consider a stochastic linear transport equation with a globally H\"{o}lder continuous and bounded vector field. Opposite to what happens in the deterministic case where shocks may appear, we show that the unique solution starting with a…

We use the full multiple scattering expansion of the retarded self-energy to obtain the gain and loss rates present in the Kadanoff-Baym relativistic transport equation. The rates we obtain include processes with any number of particles. As…

We obtain $H^{p}_{w} - L^{q}_{w^{q/p}}$ estimates for certain fractional operators.

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient…

The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…

In this paper we establish sharp weighted bounds (Buckley type theorems) for one{sided maximal and fractional integral operators in terms of one{sided $A_p$ characteristics. Appropriate sharp bounds for strong maximal functions, multiple…

We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.