### Smoothing of quasilinear parabolic operators and applications to forward-backward stochastic systems

#### Abstract

We solve the Cauchy problem for a quasilinear parabolic equation in $[0,T]\times \mathbb R^n$ with quadratic nonlinearity in the gradient and with Hölder-continuous, not necessarily differentiable, initial datum. We get the same smoothing properties of linear parabolic equations, and we use them to improve the results now available in the literature on a class of stochastic forward-backward systems.

#### Article information

Source
Adv. Differential Equations Volume 10, Number 1 (2005), 65-88.

Dates
First available in Project Euclid: 18 December 2012