English

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}
}

Comments

20

R2 v1 2026-06-22T15:14:13.464Z