Smooth critical sub-solutions of the Hamilton-Jacobi equation
نویسندگان
چکیده
منابع مشابه
Smooth critical sub-solutions of the Hamilton-Jacobi equation
We establish the existence of smooth critical sub-solutions of the HamiltonJacobi equation on compact manifolds for smooth convex Hamiltonians, that is in the context of weak KAM theory, under the assumption that the Aubry set is the union of finitely many hyperbolic periodic orbits or fixed points. Let M be a compact manifold without boundary. A function H(x, p) : T M −→ R is called a Tonelli ...
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with a special emphasis on sub-solutions. A function u :M −→ R is called a sub-solution of (HJ) if it is Lipschtiz and satisfies the inequality H(x, dux) 6 c at all its points of differentiability. Note that this definition is equivalent to the notion of viscosity sub-solutions, see [5]. We denote by C(M,R) the set of differentiable functions with Lipschitz differential. The goal of the present...
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This paper is a survey of the Hamilton-Jacobi partial differential equation. We begin with its origins in Hamilton’s formulation of classical mechanics. Next, we show how the equation can fail to have a proper solution. Setting this issue aside temporarily, we move to a problem of optimal control to show another area in which the equation arises naturally. In the final section, we present some ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2007
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2007.v14.n3.a14