The fascinating homotopy structure of Sobolev spaces

Haïm Brezis

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 3, page 207-217
  • ISSN: 1120-6330

Abstract

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We discuss recent developments in the study of the homotopy classes for the Sobolev spaces . In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].

How to cite

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Brezis, Haïm. "The fascinating homotopy structure of Sobolev spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.3 (2003): 207-217. <http://eudml.org/doc/252326>.

@article{Brezis2003,
abstract = {We discuss recent developments in the study of the homotopy classes for the Sobolev spaces $W^\{1,p\} (M;N)$. In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].},
author = {Brezis, Haïm},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Sobolev spaces; Homotopy theory; homotopy theory},
language = {eng},
month = {9},
number = {3},
pages = {207-217},
publisher = {Accademia Nazionale dei Lincei},
title = {The fascinating homotopy structure of Sobolev spaces},
url = {http://eudml.org/doc/252326},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Brezis, Haïm
TI - The fascinating homotopy structure of Sobolev spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/9//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 3
SP - 207
EP - 217
AB - We discuss recent developments in the study of the homotopy classes for the Sobolev spaces $W^{1,p} (M;N)$. In particular, we report on the work of H. Brezis - Y. Li [5] and F.B. Hang - F.H. Lin [9].
LA - eng
KW - Sobolev spaces; Homotopy theory; homotopy theory
UR - http://eudml.org/doc/252326
ER -

References

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  1. BETHUEL, F., The approximation problem for Sobolev maps between manifolds. Acta Math., 167, 1991, 153-206. Zbl0756.46017MR1120602DOI10.1007/BF02392449
  2. BOURGAIN, J. - BREZIS, H. - MIRONESCU, P., Lifting in Sobolev spaces. J. Analyse Math., 80, 2000, 37-86. Zbl0967.46026MR1771523DOI10.1007/BF02791533
  3. BREZIS, H., How to recognize constant functions. Connections with Sobolev spaces. Uspekhi Mat. Nauk (volume in honor of M. Vishik), 57, 2002, 59-74. Zbl1072.46020MR1942116DOI10.1070/RM2002v057n04ABEH000533
  4. BREZIS, H. - CORON, J.-M., Large solutions for harmonic maps in two dimensions. Comm. Math. Phys., 92, 1983, 203-215. Zbl0532.58006MR728866
  5. BREZIS, H. - LI, Y.Y., Topology and Sobolev spaces. J. Funct. Anal., 183, 2001, 321-369. Zbl1001.46019MR1844211DOI10.1006/jfan.2000.3736
  6. BREZIS, H. - LI, Y.Y. - MIRONESCU, P. - NIRENBERG, L., Degree and Sobolev spaces. Topological methods in Nonlinear Analysis, 13, 1999, 181-190. Zbl0956.46024MR1742219
  7. BREZIS, H. - NIRENBERG, L., Degree theory and BMO, Part I: compact manifolds without boundaries. Selecta Math., 1, 1995, 197-263. Zbl0852.58010MR1354598DOI10.1007/BF01671566
  8. GIAQUINTA, M. - HILDEBRANDT, S., A priori estimate for harmonic mappings. J. Reine Angew. Math., 336, 1982, 124-164. Zbl0508.58015MR671325DOI10.1515/crll.1982.336.124
  9. HANG, F.B. - LIN, F.H., Topology of Sobolev mappings II. Acta Math., to appear. Zbl1061.46032MR2082396DOI10.1090/conm/350/06343
  10. RUBINSTEIN, J. - STERNBERG, P., Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents. Comm. Math. Phys., 179, 1996, 257-263. Zbl0860.35131MR1395224
  11. SCHOEN, R. - UHLENBECK, K., Boundary regularity and the Dirichlet problem for harmonic maps. J. Differential Geom., 18, 1983, 253-268. Zbl0547.58020MR710054
  12. WHITE, B., Homotopy classes in Sobolev spaces and the existence of energy minimizing maps. Acta Math., 160, 1988, 1-17. Zbl0647.58016MR926523DOI10.1007/BF02392271

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