Regularity theory for Hamilton--Jacobi equations
The author studies the regularity and stability under small perturbations of viscosity solutions of Hamilton-Jacobi equations \(H(P+D_x u, x)=\overline{H}(P),\) where \(H(p,x):\mathbb{R}^{2n}\rightarrow \mathbb{R}\) is a strictly convex smooth Hamiltonian (\(D^{2}_{vv} L(x,v)>\gamma >0\) uniformly and coercive in \(p, \lim_{|p|\rightarrow\infty} \frac{H(p,x)}{|p|}=\infty)\), \(\mathbb{Z}^{n}\) periodic in \(x\) \((H(p,x+k)=H(p,x)\), \(k\in \mathbb{Z}^{n})\) Analogs of the KAM theorem, stability of the viscosity solutions and Mather sets under small perturbations of the Hamiltonian are proved.
scientific article; zbMATH DE number 1884226