Stochastic Analysis for the Complex Monge-Ampère Equation. (An Introduction to Krylov's Approach.)

We will prove a global viscosity comparison principle for degenerate com- plex Monge-Amp`ere equations on compact K¨ ahler manifolds and show how to combine Viscosity methods

In the case k = 0 , this theorem can be proved using the Gronwall lemma, by a method which is similar to the section about the continuity with respect to the initial condition..

We present a simple and ecient method to write short codes in vector languages for solving boundary value problem (BVP) by P 1 -Lagrange nite element meth- ods in any space

19 Observe that uniqueness of stochastic viscosity solutions then follows from the classical theory of viscosity solutions of fully non-linear second-order partial

In the pioneering papers [14,16] a deep connection between a priori estimates for solutions to Dirichlet problems relative to a class of linear elliptic equations and the

The solution to (19) cannot be calculated analytically, so an accurate approximation to the true solution was obtained by using both a very small step size and

For some compact subsets K ⊂ H −1 containing a rank-one connection, we show the rigidity property of K by imposing proper topology in the convergence of approximate solutions and

Example Itô (version 4) Taylor Solution to an SDE Quadratic covariation Multiplication rule.. Example