The Dirichlet problem for the Bellman equation at resonance

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Armstrong, Scott N.

关键词: Hamilton-Jacobi-Bellman equation;    Fully nonlinear elliptic equation;    Principal eigenvalue;    Dirichlet problem;   

DOI  :  10.1016/j.jde.2009.03.007

来源: Elsevier

【 摘 要 】

We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and positively homogeneous. Examples of such operators include the Bellman operator and the Pucci extremal operators. In the case that the two principal half-eigenvalues are not equal, we show that the measures which achieve the minimum in this formula provide a partial characterization of the solvability of the corresponding Dirichlet problem at resonance. (C) 2009 Elsevier Inc. All rights reserved.

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