Order property and modulus of continuity of weak KAM solutions. (English) Zbl 1387.37060
Summary: For the Hamilton-Jacobi equation \(H(x,\partial _xu+c)=\alpha (c)\) with \(x\in \mathbb {T}^2\), it is shown in this paper that, for all \(c\in \alpha ^{-1}(E)\) with \(E>\min \alpha \), the elementary weak KAM solutions can be parameterized so that they are \(\frac{1}{3}\)-Hölder continuous in \(C^0\)-topology.
MSC:
| 37J50 | Action-minimizing orbits and measures (MSC2010) |
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 70H20 | Hamilton-Jacobi equations in mechanics |
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