Smoothing of quasilinear parabolic operators and applications to forward-backward stochastic systems. (English) Zbl 1103.35041

The authors study the Cauchy problem for a certain quasilinear parabolic equation with quadratic nonlinearity in the gradient and with Hölder-continuous, not necessarily differentiable, initial datum, under suitable regularity and growth assumptions on the nonlinear functions involved therein. An application to stochastic forward-backward systems is also discussed.


35K55 Nonlinear parabolic equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35K15 Initial value problems for second-order parabolic equations