%0 Journal Article
%T STRONG-VISCOSITY SOLUTIONS: SEMILINEAR PARABOLIC PDEs AND PATH-DEPENDENT PDEs
%+ Alma Mater Studiorum University of Bologna (UNIBO)
%+ Unité de Mathématiques Appliquées (UMA)
%+ Optimisation et commande (OC)
%A Cosso, Andrea
%A Russo, Francesco
%@ 0030-6126
%J Osaka Journal of Mathematics
%I Osaka University
%V 56
%N 2
%P 323-373
%8 2019
%D 2019
%K strong-viscosity solutions
%K viscosity solutions
%K backward stochastic differential equations
%K path-dependent partial differential equations
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X The aim of the present work is the introduction of a viscosity type solution, called strong-viscosity solution to distinguish it from the classical one, with 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.
%G English
%Z "FMJH Program Gaspard Monge in optimization and operation research'' (Project 2014-1607H).
%2 https://ensta-paris.hal.science/hal-01145301v3/document
%2 https://ensta-paris.hal.science/hal-01145301v3/file/ComparisonViscosityOsaka2017_AcceptedDecember.pdf
%L hal-01145301
%U https://ensta-paris.hal.science/hal-01145301
%~ ENSTA
%~ INSMI
%~ UMA_ENSTA
%~ UNIV-PARIS-SACLAY
%~ ENSTA-SACLAY