Advances in Differential Equations

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

Giuseppina Guatteri and Alessandra Lunardi

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867896

Mathematical Reviews number (MathSciNet)
MR2106121

Zentralblatt MATH identifier
1103.35041

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B65: Smoothness and regularity of solutions 35K15: Initial value problems for second-order parabolic equations 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H10: Stochastic ordinary differential equations [See also 34F05]

Citation

Guatteri, Giuseppina; Lunardi, Alessandra. Smoothing of quasilinear parabolic operators and applications to forward-backward stochastic systems. Adv. Differential Equations 10 (2005), no. 1, 65--88. https://projecteuclid.org/euclid.ade/1355867896.


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