Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations. II
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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.
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