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.

Strong-viscosity solutions : classical and path-dependent PDEs / A. Cosso, F. Russo. - In: OSAKA JOURNAL OF MATHEMATICS. - ISSN 0030-6126. - 56:2(2019 Apr), pp. 323-373. [10.18910/72322]

Strong-viscosity solutions : classical and path-dependent PDEs

A. Cosso
Primo
;
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.
strong-viscosity solutions; viscosity solutions; backward stochastic differential equations; path-dependent partial differential equations
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/931962
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