Advances in Differential Equations

A generalized Osgood condition for viscosity solutions to fully nonlinear parabolic degenerate equations

Marco Papi

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Abstract

Using a generalized assumption of Osgood type, we prove a new comparison result for viscosity sub and supersolutions of fully nonlinear, possibly degenerate, parabolic equations. Our result allows to deal with hamiltonian functions with a quadratic growth in the spatial gradient, under special compatibility conditions with the diffusive terms. It applies in particular to a financial differential model for pricing Mortgage-Backed Securities.

Article information

Source
Adv. Differential Equations Volume 7, Number 9 (2002), 1125-1151.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1367241462

Mathematical Reviews number (MathSciNet)
MR1920375

Zentralblatt MATH identifier
1032.35110

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35K65: Degenerate parabolic equations 49L25: Viscosity solutions 91B28

Citation

Papi, Marco. A generalized Osgood condition for viscosity solutions to fully nonlinear parabolic degenerate equations. Adv. Differential Equations 7 (2002), no. 9, 1125--1151. https://projecteuclid.org/euclid.ade/1367241462.


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