### Abstract

We extend and clarify some of observations due to Barron and Jensen concerning the relation between subdifferentials and superdifferentials of a function and extend the comparison principle for semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians to that in infinite-dimensional Hilbert spaces.

Original language | English |
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Pages (from-to) | 137-154 |

Number of pages | 18 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 131 |

Issue number | 1 |

Publication status | Published - 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions.** / Ishii, Hitoshi.

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 131, no. 1, pp. 137-154.

}

TY - JOUR

T1 - A generalization of a theorem of Barron and Jensen and a comparison theorem for lower semicontinuous viscosity solutions

AU - Ishii, Hitoshi

PY - 2001

Y1 - 2001

N2 - We extend and clarify some of observations due to Barron and Jensen concerning the relation between subdifferentials and superdifferentials of a function and extend the comparison principle for semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians to that in infinite-dimensional Hilbert spaces.

AB - We extend and clarify some of observations due to Barron and Jensen concerning the relation between subdifferentials and superdifferentials of a function and extend the comparison principle for semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians to that in infinite-dimensional Hilbert spaces.

UR - http://www.scopus.com/inward/record.url?scp=30244536478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30244536478&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:30244536478

VL - 131

SP - 137

EP - 154

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 1

ER -