%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