Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

By Piermarco Cannarsa, Carlo Sinestrari. 2004

962 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ba11a0dcdb0636da00b7d75bebeaf5598f85790c

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In Applied Mathematics

In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

BV Estimates in Optimal Transportation and Applications (2015, background): “from [10], but for the sake of completeness we sketch its simple proof.”
On the Ma–Trudinger–Wang curvature on surfaces (2010, methodology): “The above two results can be found in [1].”
Stable solutions in potential mean field game systems (2016, methodology): “The techniques used in the paper are inspired by finite dimensional optimal control (see, for instance, in the monograph of Cannarsa and Sinestrari [4]).”
Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds (2005, background): “Another proof is given in [2], Corollary 3.”
Hamilton–Jacobi semigroup on length spaces and applications (2006, background): “ase of (viii). THE HAMILTON–JACOBI SEMIGROUP ON LENGTH SPACES AND APPLICATIONS 5 Remark 2.12. Theorem 2.5 is reminiscent of known properties of Hamilton–Jacobi equations in a smooth setting; see e.g. [5]. However, even in the context of Riemannian manifolds, we have been unable to ﬁnd exactly this s”
Sub-Riemannian interpolation inequalities (2017, background): “For deﬁnitions and alternative characterizations of locally semiconvex and semiconcave function see [CS04].”
THE DISTANCE FUNCTION FROM THE BOUNDARY IN A MINKOWSKI SPACE (2006, background): “5 in [8], where the case K = B1(0) is considered.”
Discontinuous Feedback and Nonlinear Systems (2010, background): “There are interesting systems in which f is nondifferentiable, for example when friction, diodes, or other directional phenomena are present (see for example Clarke (1983), Brogliato (1999), and Orlov (2009)).”
Optimal mass transportation and Mather theory (2004, background): “The only refinement needed is that the set of singular points of the semiconvex function φ0 is countably(d − 1)-rectifiable (see [13]).”
Semiconcavity results for optimal control problems admitting no singular minimizing controls (2008, methodology): “In order to prove the semiconcavity of the value function of optimal control problems without of state constraints one commonly applies PDE techniques based on comparison arguments, or else direct methods which use ad hoc perturbations of optimal trajectories, see, e.g., [ 8 ].”
Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games (2020, background): “is a C1,1 loc((0,T) × Mm) classical solution of (D.5), therefore in particular any point (t,q) ∈ (0,T) × Mm is regular and not conjugate (by the proof of Lemma D.1) in the sense of Deﬁnition 6.3.4 of [7]. Furthermore, let us notice that Lemma D.1 asserts that ξm(s,·) is a CN diﬀeomorphism and Theore”