Multidimensional viscosity solutions theory of semi-linear partial differential equations
Dynamical Systems
2016-08-09 v1 Analysis of PDEs
Abstract
In this study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to a type of multidimensional backward stochastic differential equations (BSDEs) is given. Further more, we establish the existence and uniqueness results for the viscosity solution of this semi-linear PDEs via the comparison theorem of the related BSDEs and a smooth approximation technique.
Keywords
Cite
@article{arxiv.1608.02204,
title = {Multidimensional viscosity solutions theory of semi-linear partial differential equations},
author = {Shuzhen Yang},
journal= {arXiv preprint arXiv:1608.02204},
year = {2016}
}
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