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arXiv · 1608.02204

Multidimensional viscosity solutions theory of semi-linear partial differential equations

Shuzhen Yang
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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.

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Shuzhen Yang. 2016-08-07. Multidimensional viscosity solutions theory of semi-linear partial differential equations. https://arxiv.org/abs/1608.02204

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