Critical points of embeddings of H 0 1 , n into Orlicz spaces

Michael Struwe

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 5, page 425-464
  • ISSN: 0294-1449

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Struwe, Michael. "Critical points of embeddings of $H^{1, n}_0$ into Orlicz spaces." Annales de l'I.H.P. Analyse non linéaire 5.5 (1988): 425-464. <http://eudml.org/doc/78160>.

@article{Struwe1988,
author = {Struwe, Michael},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Sobolev embedding; limiting exponent; local compactness; Orlicz spaces; critical exponent; loss of compactness; Yamabe problem; radially symmetric; existence; extremal functions; critical points},
language = {eng},
number = {5},
pages = {425-464},
publisher = {Gauthier-Villars},
title = {Critical points of embeddings of $H^\{1, n\}_0$ into Orlicz spaces},
url = {http://eudml.org/doc/78160},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Struwe, Michael
TI - Critical points of embeddings of $H^{1, n}_0$ into Orlicz spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 5
SP - 425
EP - 464
LA - eng
KW - Sobolev embedding; limiting exponent; local compactness; Orlicz spaces; critical exponent; loss of compactness; Yamabe problem; radially symmetric; existence; extremal functions; critical points
UR - http://eudml.org/doc/78160
ER -

References

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  2. [2] L. Carleson and S.Y.A. Chang, On the Existence of an Extremal Function for an inequality of J. Moser, Bull. des Sciences (to appear). Zbl0619.58013MR878016
  3. [3] S.K. Donaldson, An Application of Gauge Theory to Four-Dimensional Topology, J. Diff. Eq., Vol. 18, 1983, pp. 279-315. Zbl0507.57010MR710056
  4. [4] P.-L. Lions, The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, part 1, Riv. Mat. Iberoamericana, 1985. Zbl0704.49005MR834360
  5. [5] J.P. Monahan, Numerical Solution of a Non-Linear Boundary-Value Problem, Thesis, Princeton Univ., 1971. 
  6. [6] J. Moser, A Sharp Form of an Inequality by N. Trudinger, Ind. Univ. Math. J., Vol. 20, 1971, pp. 1077-1091. Zbl0213.13001MR301504
  7. [7] R.S. Palais, Critical Point Theory and the Minimax Principle, Proc. Symp. Pure Math., Vol. XV, 1970, pp. 185-212. Zbl0212.28902MR264712
  8. [8] G. Polya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton Univ. Press, 1951. Zbl0044.38301MR43486
  9. [9] J. Sacks and K. Uhlenbeck, The Existence of Minimal Immersions of 2-Spheres, Ann. Math., Vol. 113, 1981, pp. 1-24. Zbl0462.58014MR604040
  10. [10] S. Sedlacek, A Direct Method for Minimizing the Yang-Mills Functional Over 4- Manifolds, Comm. Math. Phys., Vol. 86, 1982, pp. 515-528. Zbl0506.53016MR679200
  11. [11] M. Struwe, A Global Compactness Result for Elliptic Boundary Value Problems Involving Limiting Non-Linearities, Math. Z., Vol. 187, 1984, pp. 511-517. Zbl0535.35025MR760051
  12. [12] M. Struwe, Large H-Surfaces via the Mountain-Pass-Lemma, Math. Ann., Vol. 270, 1985, pp. 441-459. Zbl0582.58010MR774369
  13. [13] M. Struwe, The Existence of Surfaces of Constant Mean Curvative with Free Boundaries, Acta Math., Vol. 160, 1988, pp. 19-64. Zbl0646.53005MR926524
  14. [14] C.H. Taubes, Path Connected Yang-Mills Moduli Spaces, J. Diff. Geom., Vol. 19, 1984, pp. 337-392. Zbl0551.53040MR755230
  15. [15] N.S. Trudinger, On Imbeddings into Orlicz Spaces and Some Applications, J. Math. Mech., Vol. 17, 1967, pp. 473-484. Zbl0163.36402MR216286
  16. [16] H.C. Wente, Large Solutions to the Volume Constrained Plateau Problem, Arch. Rat. Mech. Anal., vol. 75, 1980, pp. 59-77. Zbl0473.49029MR592104

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