A probabilistic approach to interior regularity of fully nonlinear degenerate elliptic equations in smooth domains

Details A probabilistic approach to interior regularity of fully nonlinear degenerate elliptic equations in smooth domains A probabilistic approach to interior regularity of fully nonlinear degenerate elliptic equations in smooth domains

2011-12-24

arxiv.org/abs/1112.5692v1

Mathematics

Probability

29 pages

Scientific paper

We consider probabilistic solutions to Dirichlet problems for degenerate Bellman equations, given by value functions of controlled diffusion processes. We investigate the regularity and estimate the derivatives up to second order of the value function, under the assumption of non-degeneracy along the normal to the boundary and an interior condition weaker than the non-degeneracy. The value function is the unique solution to the associated Dirichlet problem in our setting. Our approach is probabilistic.

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