A free boundary problem in variational inequality with gradient constraint

doi:10.3969/j.issn.1000-5641.2018.01.001

Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (1): 1-10.doi: 10.3969/j.issn.1000-5641.2018.01.001

A free boundary problem in variational inequality with gradient constraint

GUAN Chong-hu¹, CHEN Jing²

1. School of Mathematics, Jiaying University, Meizhou Guangdong 514015, China;
2. School of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong 999077, China

Received:2017-02-15 Online:2018-01-25 Published:2018-01-11

Abstract

Abstract: Consider a parabolic variational inequality with gradient constraint
min{vt-1/2σ²v_xx-μv_x+cv,v_x-1}=0.
The problem stems from a stochastic optimal control problem based on optimal dividend model. By using PDE technique and the penalty method, the existence and uniqueness and some a priori estimates of the solution of the variational inequality are obtained, and then the properties of the free boundary are further discussed. It is proved that the free boundary can be expressed as a function of x with respect to t and is a monotonically increasing, C^∞ smooth curve starting from zero.

Key words: gradient constraint, variational inequality, free boundary, stochastic optimal control, optimal dividend

CLC Number:

O157.26

GUAN Chong-hu, CHEN Jing. A free boundary problem in variational inequality with gradient constraint[J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 1-10.

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A free boundary problem in variational inequality with gradient constraint

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