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April 2019 STRONG-VISCOSITY SOLUTIONS: CLASSICAL AND PATH-DEPENDENT PDEs
Andrea Cosso, Francesco Russo
Osaka J. Math. 56(2): 323-373 (April 2019).

Abstract

The aim of the present work is the introduction of a viscosity type solution, called $strong$-$viscosity$ $solution$ emphasizing also a similarity with the existing notion of $strong$ $solution$ in the literature. It has the following peculiarities: it is a purely analytic object; it can be easily adapted to more general equations than classical partial differential equations. First, we introduce the notion of strong-viscosity solution for semilinear parabolic partial differential equations, defining it, in a few words, as the pointwise limit of classical solutions to perturbed semilinear parabolic partial differential equations; we compare it with the standard definition of viscosity solution. Afterwards, we extend the concept of strong-viscosity solution to the case of semilinear parabolic path-dependent partial differential equations, providing an existence and uniqueness result.

Citation

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Andrea Cosso. Francesco Russo. "STRONG-VISCOSITY SOLUTIONS: CLASSICAL AND PATH-DEPENDENT PDEs." Osaka J. Math. 56 (2) 323 - 373, April 2019.

Information

Published: April 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07080088
MathSciNet: MR3934979

Subjects:
Primary: 35D40, 35R15, 60H10, 60H30

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 2 • April 2019
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