The aim of the present work is the introduction of a viscosity type solution, called strongviscosity 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.

Cosso A., Russo F. (2019). Strong-viscosity solutions: Classical and path-dependent pdes. OSAKA JOURNAL OF MATHEMATICS, 56(2), 323-373.

Strong-viscosity solutions: Classical and path-dependent pdes

Cosso A.;
2019

Abstract

The aim of the present work is the introduction of a viscosity type solution, called strongviscosity 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.
2019
Cosso A., Russo F. (2019). Strong-viscosity solutions: Classical and path-dependent pdes. OSAKA JOURNAL OF MATHEMATICS, 56(2), 323-373.
Cosso A.; Russo F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/698221
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