Abstract
AbstractThis is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton–Jacobi equations in the past decades. We also review further applications of the theory to various fields such as Riemannian geometry, Hamiltonian dynamical systems and partial differential equations.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Istituto Nazionale di Alta Matematica “Francesco Severi”
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Reference84 articles.
1. Attouch, H., Azé, D.: Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method. Ann. Inst. H. Poincaré Anal. Non Linéaire 10(3), 289–312 (1993)
2. Alberti, G., Ambrosio, L., Cannarsa, P.: On the singularities of convex functions. Manuscripta Math. 76(3–4), 421–435 (1992)
3. Albano, P., Cannarsa, P.: Structural properties of singularities of semiconcave functions. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28(4), 719–740 (1999)
4. Albano, P., Cannarsa, P.: Propagation of singularities for concave solutions of Hamilton-Jacobi equations. In: International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), pp. 583–588. World Sci. Publ., River Edge, NJ, (2000)
5. Albano, P., Cannarsa, P.: Propagation of singularities for solutions of nonlinear first order partial differential equations. Arch. Ration. Mech. Anal. 162(1), 1–23 (2002)
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