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- W2963928752 abstract "We study quantitative estimates of compactness in W 1;1 loc for the map St, t > 0 that associates to every given initial data u0 2 Lip(R N ) the corresponding solution Stu0 of a Hamilton-Jacobi equation ut +H x;rxu = 0; t 0; x2 R N ; with a convex and coercive Hamiltonian H = H(x;p). We provide upper and lower bounds of order 1= N on the the Kolmogorov -entropy in W 1;1 of the image through the map St of sets of bounded, compactly supported initial data. Quantitative estimates of compactness, as suggested by P.D. Lax [23], could provide a measure of the order of resolution and of complexity of a numerical method implemented for this equation. We establish these estimates deriving accurate a-priori bounds on the Lipschitz, semiconcavity and semiconvexity constant of a viscosity solution when the initial data is semiconvex. The derivation of a small time controllability result is also fundamental to establish the lower bounds on the -entropy." @default.
- W2963928752 created "2019-07-30" @default.
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- W2963928752 date "2015-01-01" @default.
- W2963928752 modified "2023-09-27" @default.
- W2963928752 title "Compactness estimates for Hamilton-Jacobi equations depending on space" @default.
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