### Abstract

In this paper we review some representation formulas for viscosity solutions in terms of certain variational problems, following an approach due to (Fleming and Vermes, SIAM J Control Optim 27(5):1136-1155, 1989).We consider both the discounted cost infinite horizon problem and the terminal value problem. These formulas are obtained using a relaxed control formulation and then applying duality theory.

Original language | English |
---|---|

Pages (from-to) | 361-386 |

Number of pages | 26 |

Journal | Springer Proceedings in Mathematics |

Volume | 2 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

Externally published | Yes |

### Fingerprint

### Cite this

}

**Duality theory, representation formulas and uniqueness results for viscosity solutions of hamilton-jacobi equations.** / Gomes, Diogo A.; Valdinoci, Enrico.

Research output: Contribution to journal › Review article

TY - JOUR

T1 - Duality theory, representation formulas and uniqueness results for viscosity solutions of hamilton-jacobi equations

AU - Gomes, Diogo A.

AU - Valdinoci, Enrico

PY - 2011/1/1

Y1 - 2011/1/1

N2 - In this paper we review some representation formulas for viscosity solutions in terms of certain variational problems, following an approach due to (Fleming and Vermes, SIAM J Control Optim 27(5):1136-1155, 1989).We consider both the discounted cost infinite horizon problem and the terminal value problem. These formulas are obtained using a relaxed control formulation and then applying duality theory.

AB - In this paper we review some representation formulas for viscosity solutions in terms of certain variational problems, following an approach due to (Fleming and Vermes, SIAM J Control Optim 27(5):1136-1155, 1989).We consider both the discounted cost infinite horizon problem and the terminal value problem. These formulas are obtained using a relaxed control formulation and then applying duality theory.

UR - http://www.scopus.com/inward/record.url?scp=84904119962&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14788-3_28

DO - 10.1007/978-3-642-14788-3_28

M3 - Review article

VL - 2

SP - 361

EP - 386

JO - Springer Proceedings in Mathematics

JF - Springer Proceedings in Mathematics

SN - 2190-5614

ER -