### Abstract

The existence theorems for (1) a differential inclusion in a Banach space and (2) a variational problem governed by it are presented. In order to solve this problem, some implications of the weak convergence in the space of vector-valued absolutely continuous functions are also explored.

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

Pages (from-to) | 5-10 |

Number of pages | 6 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 77 |

Issue number | 1 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Convex normal integrand
- Differential inclusion
- Lower compactness property
- Vector-valued absolutely continuous function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A generalization of the weak convergence theorem in Sobolev spaces with application to differential inclusions in a Banach space.** / Maruyama, Toru.

Research output: Contribution to journal › Article

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 77, no. 1, pp. 5-10.

}

TY - JOUR

T1 - A generalization of the weak convergence theorem in Sobolev spaces with application to differential inclusions in a Banach space

AU - Maruyama, Toru

PY - 2001

Y1 - 2001

N2 - The existence theorems for (1) a differential inclusion in a Banach space and (2) a variational problem governed by it are presented. In order to solve this problem, some implications of the weak convergence in the space of vector-valued absolutely continuous functions are also explored.

AB - The existence theorems for (1) a differential inclusion in a Banach space and (2) a variational problem governed by it are presented. In order to solve this problem, some implications of the weak convergence in the space of vector-valued absolutely continuous functions are also explored.

KW - Convex normal integrand

KW - Differential inclusion

KW - Lower compactness property

KW - Vector-valued absolutely continuous function

UR - http://www.scopus.com/inward/record.url?scp=23044525208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044525208&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044525208

VL - 77

SP - 5

EP - 10

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 1

ER -