This is a preview of subscription content, log in via an institution to check access.
References
R.A. Adams.Sobolev spaces. Academic Press, 1975.
F. Bethuel.The approximation problem for Sobolev maps between two manifolds. Acta Math.,167 (1991), 153–206.
F. Bethuel.Approximation in trace spaces defined between manifolds, Nonlinear Analysis, T.M.A.24 (1995), 121–130.
F. Bethuel, H. Brezis and F. Hélein.Ginzburg-Landau Vortices. Birkhäuser, 1994.
F. Bethuel and X. Zheng.Density of smooth functions between two manifolds in Sobolev spaces. J. Funct. Anal.,80 (1988), 60–75.
A. Boutet de Monvel-Berthier, V. Georgescu and R. Purice.A boundary value problem related to the Ginzburg-Landau model. Comm. Math. Phys.,142 (1991), 1–23.
H. Brezis.Lectures on the Ginzburg-Landau Vortices. Scuola Normale Superiore, Pisa, 1995.
H. Brezis.Large harmonic maps in two dimensions in Nonlinear Variational Problems, A. Marino et al. ed., Pitman, 1985.
H. Brezis and J. M. Coron.Large solutions for harmonic maps in two dimensions. Comm. Math. Phys.,92 (1983), 203–215.
R. R. Coifman and Y. Meyer.Une généralisation du théorème de Calderón sur l'intégrale de Cauchy in Fourier Analysis, Proc. Sem. at El Escorial, Asoc. Mat. Española, Madrid, 1980, 88–116.
H. A. De Kleine and J. E. Girolo.A degree theory for almost continuous maps. Fund. Math.,101 (1978), 39–52.
F. Demengel. Une Caractérisation des applications deW 1,p (B N,S 1)qui peuvent être approchées par des fonctions régulières. C.R.A.S.,30 (1990), 553–557.
M. P. do Carmo.Riemannian geometry. Birkhäuser, 1992.
R. G. Douglas.Banach Algebra Techniques in Operator Theory. Acad. Press, 1972.
M. J. Esteban and S. Müller.Sobolev maps with integer degree and applications to Skyrme's problem. Proc. Roy. Soc. London,436 A, 1992, 197–201.
M. Giaquinta, G. Modica and J. Soucek.Remarks on the degree theory. J. Funct. Anal.,125 (1994), 172–200.
O. H. Hamilton.Fixed points for certain noncontinuous transformations. Proc. Amer. Math. Soc.,8 (1957), 750–756.
F. John and L. Nirenberg.On functions of bounded mean oscillation. Comm. Pure Appl. Math.,14 (1961), 415–426.
J. Nash.Generalized Brouwer theorem, Research Problems. Bull. Amer. Math. Soc.,62 (1956), 76.
L. Nirenberg.Topics in Nonlinear Functional Analysis. Courant Institute Lecture Notes, 1974.
H. M. Reimann.Functions of bounded mean oscillation and quasi-conformal mappings. Comm. Math. Helv.,49 (1974), 260–276.
D. Sarason.Functions of vanishing mean oscillation. Trans. Amer. Math. Soc.,207 (1975), 391–405.
R. Schoen and K. Uhlenbeck.Boundary regularity and the Dirichlet problem for harmonic maps. J. Diff. Geom.,18 (1983), 253–268.
J. Stallings.Fixed point theorems for connectivity maps. Fund. Math.,47 (1959), 249–263.
D. Stegenga.Bounded Toeplitz operators on H 1 and applications of the duality between H 1 and the functions of bounded mean oscillations. Amer. J. Math.,98 (1976), 573–589.
E. Stein.Harmonic Analysis. Princeton University Press, 1993.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brezis, H., Nirenberg, L. Degree theory and BMO; part I: Compact manifolds without boundaries. Selecta Mathematica, New Series 1, 197–263 (1995). https://doi.org/10.1007/BF01671566
Issue Date:
DOI: https://doi.org/10.1007/BF01671566