Acta Applicandae Mathematica

, Volume 46, Issue 1, pp 29–48 | Cite as

Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations. II

  • G. V. Nosovskij


A formal method of constructing the viscosity solutions for abstract nonlinear equations of Hamilton–Jacobi–Bellman (HJB) type was developed in the previous work of the author. A new advantage of this method (which was called an ‘nonlinear potentials’ method) is that it gives a possibility to choose at the first step an expected regularity of the solution and then – to construct this solution. This makes the whole procedure more simple because an analysis of regularity of viscosity solutions is usually the most complicated step.

Nonlinear potentials method is a generalization of Krylov's approach to study HJB equations.

In this article nonlinear potentials method is applied to elliptic degenerate HJB equations in Rd with variable coefficients.

Hamilton–Jacobi–Bellman equations nonlinear potentials nonlinear PDE viscosity solutions optimal control 


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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • G. V. Nosovskij
    • 1
  1. 1.Laboratory of Computer Methods in Natural and Human SciencesMoscow State UniversityMoscowRussia

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