In this paper, we derive a priori interior Hessian estimates for the Lagrangian mean curvature equation if phase is supercritical and has bounded second derivatives.

We study the non–linear dynamics of self–gravitating irrotational dust in a general relativistic framework, using synchronous and comoving (i.e. Lagrangian) coordinates. All the equations are written in terms of a single tensor variable, the metric tensor of the spatial sections orthogonal to the fluid flow. This treatment allows an unambiguous expansion in inverse (even) powers of the speed of...

We present a Lagrangian for the bilinear discrete KP (or HirotaMiwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in [8] in a higher dimensional case.

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.

Contents 1. Introduction 1 2. Reminders on the Cauchy-Lipschitz theory 4 3. Nonsmooth vector fields in Euclidean spaces 4 4. Abstract setup 7 5. Derivations and their regularity 10 6. Eulerian side 11 6.1. Existence of solutions to the continuity equation 11 6.2. Uniqueness of solutions to the continuity equation 14 7. Lagrangian side 16 7.1. ODE's associated to derivations and Regular Lagrangi...

The exact unclosed equation for the phase-space density function ~or corresponding Lagrangian pdf! in turbulent flows is obtained using conditional techniques. The equation has direct implications for stochastic Lagrangian models based on the assumption of similarity with a Markov process. The problem of random particle sources is examined and the appropriate correcting term is suggested. © 199...

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some ...

We prove enhanced error estimates for high order semi-lagrangian discretizations of the Vlasov-Poisson equation. It provides new insights into optimal numerical strategies for the numerical solution of this problem. The new error estimate O ( min ( ∆x ∆t , 1 ) ∆x + ∆t ) is based on advanced error estimates for semi-lagrangian schemes, also equal to shifted Strang’s schemes, for the discretizati...

The valuation of a gas storage facility is characterized as a stochastic control problem, resulting in a Hamilton-Jacobi-Bellman (HJB) equation. In this paper, we present a semi-Lagrangian method for solving the HJB equation for a typical gas storage valuation problem. The method is able to handle a wide class of spot price models that exhibit mean-reverting, seasonality dynamics and price jump...

A new method is developed to solve the condensation equation as it relates to air quality models using both semi-Lagrangian and Lagrangian  uxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, partitioned  ux integrated semi-Lagrangian method (PFISLM), can be used with lower-order interpolators and produces highly accurate...