### Abstract

This paper addresses some topological and analytical issues concerning Sobolev mappings between compact Riemannian manifolds. Among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of Brezis and Li. In particular we solved two conjectures in [BL]. We also give a topological obstruction for the weak sequential density of smooth maps in a given Sobolev mapping space. Finally we show a necessary and sufficient topological condition under which the smooth maps are strongly dense in the Sobolev spaces. The earlier result, Theorem 1 of [B2], was shown to be not correct.

Original language | English (US) |
---|---|

Pages (from-to) | 321-330 |

Number of pages | 10 |

Journal | Mathematical Research Letters |

Volume | 8 |

Issue number | 3 |

State | Published - 2001 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*8*(3), 321-330.

**Topology of Sobolev mappings.** / Hang, Fengbo; Lin, Fang-Hua.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 8, no. 3, pp. 321-330.

}

TY - JOUR

T1 - Topology of Sobolev mappings

AU - Hang, Fengbo

AU - Lin, Fang-Hua

PY - 2001

Y1 - 2001

N2 - This paper addresses some topological and analytical issues concerning Sobolev mappings between compact Riemannian manifolds. Among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of Brezis and Li. In particular we solved two conjectures in [BL]. We also give a topological obstruction for the weak sequential density of smooth maps in a given Sobolev mapping space. Finally we show a necessary and sufficient topological condition under which the smooth maps are strongly dense in the Sobolev spaces. The earlier result, Theorem 1 of [B2], was shown to be not correct.

AB - This paper addresses some topological and analytical issues concerning Sobolev mappings between compact Riemannian manifolds. Among the results we obtained are unified proofs of various generalizations of results obtained in a recent work of Brezis and Li. In particular we solved two conjectures in [BL]. We also give a topological obstruction for the weak sequential density of smooth maps in a given Sobolev mapping space. Finally we show a necessary and sufficient topological condition under which the smooth maps are strongly dense in the Sobolev spaces. The earlier result, Theorem 1 of [B2], was shown to be not correct.

UR - http://www.scopus.com/inward/record.url?scp=0035535889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035535889&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 321

EP - 330

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 3

ER -