A Generalized Osgood Condition for Viscosity Solutions to Fully Nonlinear Parabolic Degenerate Equations

نویسنده

  • Marco Papi
چکیده

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 MortgageBacked Securities.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Introduction to fully nonlinear parabolic equations

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...

متن کامل

Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems

We obtain new oscillation and gradient bounds for the viscosity solutions of fully nonlinear degenerate elliptic equations where the Hamiltonian is a sum of a sublinear and a superlinear part in the sense of Barles and Souganidis (2001). We use these bounds to study the asymptotic behavior of weakly coupled systems of fully nonlinear parabolic equations. Our results apply to some “asymmetric sy...

متن کامل

Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Equations

Using the maximum principle for semicontinuous functions (Differential Integral Equations 3 (1990), 1001–1014; Bull. Amer. Math. Soc. (N.S) 27 (1992), 1–67), we establish a general ‘‘continuous dependence on the nonlinearities’’ estimate for viscosity solutions of fully nonlinear degenerate parabolic equations with timeand space-dependent nonlinearities. Our result generalizes a result by Souga...

متن کامل

ar X iv : 0 90 6 . 14 58 v 1 [ m at h . A P ] 8 J un 2 00 9 DIFFERENCE - QUADRATURE SCHEMES FOR NONLINEAR DEGENERATE PARABOLIC INTEGRO - PDE

We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...

متن کامل

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain

We establish comparison and existence theorems of viscosity solutions of the initial-boundary value problem for some singular degenerate parabolic partial di/erential equations with nonlinear oblique derivative boundary conditions. The theorems cover the capillary problem for the mean curvature 1ow equation and apply to more general Neumann-type boundary problems for parabolic equations in the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999