A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains

Journal Article · Sat Jun 15 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-013-9194-4· OSTI ID:22163085

Zhou Wei, E-mail: [e-mail] ^[1]

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1. University of Minnesota, School of Mathematics (United States)

We consider the value function of a stochastic optimal control of degenerate diffusion processes in a domain D. We study the smoothness of the value function, under the assumption of the non-degeneracy of the diffusion term along the normal to the boundary and an interior condition weaker than the non-degeneracy of the diffusion term. When the diffusion term, drift term, discount factor, running payoff and terminal payoff are all in the class of C{sup 1,1}( D-bar ) , the value function turns out to be the unique solution in the class of C{sub loc}{sup 1,1}(D) Intersection C{sup 0,1}( D-bar ) to the associated degenerate Bellman equation with Dirichlet boundary data. Our approach is probabilistic.

• OSTI ID: 22163085
• Journal Information: Applied Mathematics and Optimization, Vol. 67, Issue 3; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
DIFFUSION
DIRICHLET PROBLEM
EQUATIONS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
OPTIMAL CONTROL
PROBABILISTIC ESTIMATION
STOCHASTIC PROCESSES