Stationary p-harmonic maps into spheres

• Autorzy: Paweł Strzelecki
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 383-393

Daty

wydano

1996

Twórcy

autor

Paweł Strzelecki

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] F. Bethuel, On the singular set of stationary harmonic maps, Manuscripta Math. 78 (1992), 417-443.
• [2] R. Coifman, P. Lions, Y. Meyer and S. Semmes, Compensated compactness and Hardy spaces, Cahiers Mathématiques de la Décision, preprint no. 9123, CEREMADE.
• [3] R. Coifman, P. Lions, Y. Meyer and S. Semmes, Compacité par compensation et espaces de Hardy, C. R. Acad. Sci. Paris 309 (1989), 945-949.
• [4] L. C. Evans, Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal. 116 (1991), 101-113.
• [5] C. Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 585-587.
• [6] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
• [7] M. Fuchs, The blow-up of p-harmonic maps, Manuscripta Math., to appear.
• [8] M. Fuchs, Some regularity theorems for mappings which are stationary points of the p-energy functional, Analysis 9 (1989), 127-143.
• [9] M. Fuchs, p-harmonic obstacle problems. I: Partial regularity theory, Ann. Mat. Pura Appl. 156 (1990), 127-158.
• [10] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, Elsevier, 1985.
• [11] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, 1983.
• [12] R. Hardt and F. H. Lin, Mappings minimizing the $L^p$-norm of the gradient, Comm. Pure Appl. Math. 40 (1987), 555-588.
• [13] F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une sphère, C. R. Acad. Sci. Paris 311 (1990), 519-524.
• [14] F. Hélein, Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne, ibid. 312 (1991), 591-596.
• [15] F. Hélein, Regularity of weakly harmonic maps from a surface into a manifold with symmetries, Manuscripta Math. 70 (1991), 203-218.
• [16] S. Luckhaus, Partial Hölder continuity for minima of certain energies among maps into a Riemannian manifold, Indiana Univ. Math. J. 37 (1988), 346-367.
• [17] S. Müller, Higher integrability of determinants and weak convergence in $L^1$, J. Reine Angew. Math. 412 (1990), 20-34.
• [18] P. Price, A monotonicity formula for Yang-Mills fields, Manuscripta Math. 43 (1983), 131-166.
• [19] T. Rivière, Everywhere discontinuous harmonic maps from the dimension 3 into spheres, Centre des Mathématiques et Leurs Applications, ENS-Cachan, preprint no. 9302.
• [20] R. Schoen and K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335.
• [21] P. Strzelecki, Regularity of p-harmonic maps from the p-dimensional ball into a sphere, Manuscripta Math., to appear.
• [22] H. Takeuchi, Some conformal properties of p-harmonic maps and a regularity for sphere-valued p-harmonic maps, J. Math. Soc. Japan 46 (1994), 217-234.
• [23] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), 126-150.
• [24] A. Torchinsky, Real-Variable Methods in Analysis, Academic Press, 1986.
• [25] T. Toro and Ch. Wang, Compactness properties of weakly p-harmonic maps into homogeneous spaces, Indiana Univ. Math. J. 44 (1995), 87-114.
• [26] K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), 219-240.
• [27] N. Uraltseva, Degenerate quasilinear elliptic systems, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 7 (1968), 184-222.
• [28] W. P. Ziemer, Weakly Differentiable Functions, Grad. Texts in Math. 120, Springer, 1989.