Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Optimal stochastic switching and the Dirichlet problem for the Bellman equation

Authors: Lawrence C. Evans and Avner Friedman
Journal: Trans. Amer. Math. Soc. 253 (1979), 365-389
MSC: Primary 93E20
MathSciNet review: 536953
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {L^i}$ be a sequence of second order elliptic operators in a bounded n-dimensional domain $ \Omega $, and let $ {f^i}$ be given functions. Consider the problem of finding a solution u to the Bellman equation $ {\sup _i}({L^i}u\, - \,{f^i})\, = \,0$ a.e. in $ \Omega $, subject to the Dirichlet boundary condition $ u\, = \,0$ on $ \partial \Omega $. It is proved that, provided the leading coefficients of the $ {L^i}$ are constants, there exists a unique solution u of this problem, belonging to $ {W^{1,\infty }}(\Omega )\, \cap \,W_{{\text{loc}}}^{2,\infty }(\Omega )$. The solution is obtained as a limit of solutions of certain weakly coupled systems of nonlinear elliptic equations; each component of the vector solution converges to u. Although the proof is entirely analytic, it is partially motivated by models of stochastic control. We solve also certain systems of variational inequalities corresponding to switching with cost.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 93E20

Retrieve articles in all journals with MSC: 93E20

Additional Information

PII: S 0002-9947(1979)0536953-4
Keywords: Bellman equation, elliptic operators, nonlinear elliptic equation, accretive operators, stochastic differential equations
Article copyright: © Copyright 1979 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia