HOLDER ESTIMATES FOR DEGENERATE ELLIPTIC EQUATIONS WITH COERCIVE HAMILTONIANS

作者：Dolcetta I Capuzzo^*; Leoni F; Porretta A

来源：Transactions of the American Mathematical Society, 2010, 362(9): 4511-4536.

• Degenerate elliptic equations
• coercive Hamiltonians
• Holder regularity
• viscosity (sub)solutions

We prove a priori estimates and regularity results for some quasi-linear degenerate elliptic equations arising in optimal stochastic control problems. Our main results show that strong coerciveness of gradient terms forces bounded viscosity subsolutions to be globally Holder continuous, and solutions to be locally Lipschitz continuous. We also give an existence result for the associated Dirichlet problem.

• 出版日期2010-9