# Balanced split sets and Hamilton-Jacobi equations

## Related Articles

- SBV Regularity for Hamilton-Jacobi Equations in $${{\mathbb R}^n}$$. Bianchini, Stefano; De Lellis, Camillo; Robyr, Roger // Archive for Rational Mechanics & Analysis;Jun2011, Vol. 200 Issue 3, p1003
In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations In particular, under the assumption that the Hamiltonian $${H\in C^2({\mathbb R}^n)}$$ is uniformly convex, we prove that D u and âˆ‚ u belong to the class SBV(Î©).

- Value functions for certain class of Hamilton Jacobi equations. BISWAS, ANUP; DUTTA, RAJIB; ROY, PROSENJIT // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Aug2011, Vol. 121 Issue 3, p349
We consider a class of Hamilton Jacobi equations (in short, HJE) of type in â„Ã—â„ and m > 1, with bounded, Lipschitz continuous initial data. We give a Hopf-Lax type representation for the value function and also characterize the set of minimizing paths. It is shown that the...

- About an Optimal Visiting Problem. Bagagiolo, Fabio; Benetton, Michela // Applied Mathematics & Optimization;Feb2012, Vol. 65 Issue 1, p31
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its...

- Metric viscosity solutions of Hamilton-Jacobi equations depending on local slopes. Gangbo, Wilfrid; Święch, Andrzej // Calculus of Variations & Partial Differential Equations;Sep2015, Vol. 54 Issue 1, p1183
We continue the study of viscosity solutions of Hamilton-Jacobi equations in metric spaces initiated in []. We present a more complete account of the theory of metric viscosity solutions based on local slopes. Several comparison and existence results are proved and the main techniques for such...

- Viscosity solutions methods for converse KAM theory. Diogo Gomes; Adam Oberman // ESAIM: Mathematical Modelling & Numerical Analysis;Nov2008, Vol. 42 Issue 6, p1047
The main objective of this paper is to prove new necessary conditions to the existence of KAM tori. To do so, we develop a set of explicit a-priori estimates for smooth solutions of Hamilton-Jacobi equations, using a combination of methods from viscosity solutions, KAM and Aubry-Mather theories....

- Existence of C1 critical subsolutions of the Hamilton-Jacobi equation. Fathi, Albert; Siconolfi, Antonio // Inventiones Mathematicae;Feb2004, Vol. 155 Issue 2, p363
Analyzes the existence of critical subsolutions of the Hamilton-Jacobi equations. Definition of viscosity subsolution, supersolution and solution; Analysis of triangle inequalities; Assessment of the behavior of Euler-Lagrange flow.

- Long-time Behavior of Solutions of Hamiltonâ€“Jacobi Equations with Convex and Coercive Hamiltonians. ICHIHARA, NAOYUKI; ISHII, HITOSHI; LIONS, P.-L. // Archive for Rational Mechanics & Analysis;Nov2009, Vol. 194 Issue 2, p383
We investigate the long-time behavior of viscosity solutions of Hamiltonâ€“Jacobi equations in $${\mathbb{R}^n}$$ with convex and coercive Hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity. We apply the criteria to...

- Viscosity Solutions with Asymptotic Behavior of Hessian Quotient Equations. Limei Dai // International Proceedings of Computer Science & Information Tech;2012, Vol. 44, p65
In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to Hessian quotient equations.

- PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians. Fathi, Albert; Siconolfi, Antonio // Calculus of Variations & Partial Differential Equations;Feb2005, Vol. 22 Issue 2, p185
We propose a PDE approach to the Aubry-Mather theory using viscosity solutions. This allows to treat Hamiltonians (on the flat torus) just coercive, continuous and quasiconvex, for which a Hamiltonian flow cannot necessarily be defined. The analysis is focused on the family of Hamilton-Jacobi...