@article{AIHPC_1998__15_6_725_0,
author = {M\"uller, Stefan and Struwe, Micha\"el and Freire, Alexandre},
title = {Weak compactness of wave maps and harmonic maps},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {15},
year = {1998},
pages = {725-754},
mrnumber = {1650966},
zbl = {0924.58011},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1998__15_6_725_0}
}
Müller, Stefan; Struwe, Michael; Freire, Alexandre. Weak compactness of wave maps and harmonic maps. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) pp. 725-754. http://gdmltest.u-ga.fr/item/AIHPC_1998__15_6_725_0/
[1] and , Weak limits of solutions to the steady incompressible
two-dimensional Euler equations in a bounded domain, Asympt. Anal., Vol. 8, 1994, pp. 277-291. | MR 1288610 | Zbl 0808.76014
[2] , Weak convergence of Palais-Smale sequences for some critical functionals, Calc. Var., Vol. 1, 1993, pp. 267-310. | MR 1261547 | Zbl 0812.58018
[3] , On the singular set of stationary harmonic maps, manusc. math., Vol. 78, 1993, pp. 417-443. | MR 1208652 | Zbl 0792.53039
[4] , Sistemi ellittiche del secondo ordine e spazi L2.λ, Ann. Mat. Pura Appl., Vol. 69, 1965, pp. 321-380. | MR 192168 | Zbl 0145.36603
[5] and , On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1041-1091. | MR 1223662 | Zbl 0744.58071
[6] , , and , Compensated compactness and Hardy spaces, J. Math. Pures Appl., Vol. 72, 1993, pp. 247-286. | MR 1225511 | Zbl 0864.42009
[7] and , Reduced Hausdorff dimension and concentration cancellation for two-dimensional incompressible flows, J. Amer. Math. Soc., Vol. 1. 1988, pp. 59-95. | MR 924702 | Zbl 0707.76026
[8] , Partial regularity for stationary harmonic maps into spheres, Arch. Rat. Mech. Anal., Vol. 116, 1991, 101-113. | MR 1143435 | Zbl 0754.58007
[9] and , Hp spaces of several variables, Acta Math., Vol. 129, 1972, pp. 137-193. | MR 447953 | Zbl 0257.46078
[10] , Capacity methods in the theory of partial differential equations, Jahresb. Dt. Math. Ver., Vol. 84, 1982, pp. 1-44. | MR 644068 | Zbl 0486.35002
[11] , Global weak solutions of the wave map system to compact homogeneous spaces, manuscripta math., Vol. 91, 1996, pp. 525-533. | MR 1421290 | Zbl 0867.58019
[12] , and , Weak convergence of wave maps from (2+1) dimensional Minkowski space to Riemannian manifolds, Invent. Math., Vol. 130, 1997, pp. 589-617. | MR 1483995 | Zbl 0906.35061
[13] , Introduction to regularity theory for nonlinear elliptic systems, Lectures in Mathematics, Birkhäuser, 1993. | MR 1239172 | Zbl 0786.35001
[14] , A local version of the Hardy space, Duke Math. J., Vol. 46, 1979, pp. 27-42. | MR 523600 | Zbl 0409.46060
[15] , Elementare Bemerkung zur isoperimetrischen Ungleichung im R3, Math. Z., Vol. 132, 1973, pp. 319-322. | MR 323976 | Zbl 0251.52014
[16] , Régularité des applications faiblement harmoniques entre une surface et une variété Riemannienne, C. R. Acad. Sci. Paris Ser. I Math., Vol. 312, 1991, pp. 591-596. | MR 1101039 | Zbl 0728.35015
[17] and , Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1221-1268. | MR 1231427 | Zbl 0803.35095
[18] and , Smoothing estimates for null forms and applications, Int. Math. Res. Not., Vol. 4, 1994, pp. 383-389. | MR 1301438 | Zbl 0832.35096
[19] , The concentration compactness principle in the calculus of variations, the limit case, Part 2 , Rev. Mat. Iberoam., Vol. 1/2 , 1985, pp. 45-121. | MR 850686 | Zbl 0704.49006
[20] , An estimate on the Hausdorff dimension of a concentration set for the incompressible 2-D Euler equations, Indiana Univ. Math. J., Vol. 43, 1994, pp. 521-534. | MR 1291527 | Zbl 0807.35113
[21] and , Global existence of wave maps in 1+2 dimensions for finite energy data, Top. Methods Nonlinear Analysis, Vol. 7, 1996, pp. 245-259. | MR 1481698 | Zbl 0896.35086
[22] , and , Harmonic maps on planar lattices, Ann. SNS Pisa, to appear. | Numdam
[23] and , Spatially discrete wave maps on (1+2)-dimensional space-time, Top. Methods Nonlinear Analysis, to appear. | Zbl 0933.58020
[24] , A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Conun. P.D.E., Vol. 19, 1994, 277-319. | MR 1257006 | Zbl 0836.35030
[25] , Weak solutions and development of singularities in the SU (2) σ-model, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 459-469. | MR 933231 | Zbl 0686.35081
[26] and , On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 947-971. | MR 1168115 | Zbl 0769.58015
[27] , Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970. | MR 290095 | Zbl 0207.13501
[28] , Harmonic analysis, Princeton Univ. Press, 1993. | MR 1232192 | Zbl 0821.42001
[29] , Wave maps, in: Nonlinear partial differential equations in geometry and physics-Barrett Lectures 1995 (Eds. G. Baker et al.), Birkhäuser, 1997, pp. 113-153. | MR 1437153 | Zbl 0869.53017
[30] , Remarks on oscillations and Stokes's equation, in: Macroscopic modelling of turbulent flows (Nice, 1984), Lect. Notes Phys., Vol. 230, Springer, 1985, pp. 24-31. | MR 815930 | Zbl 0611.76042
[31] , An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl., Vol. 26, 1969, pp. 318-344. | MR 243467 | Zbl 0181.11501
[32] , Regularity of solutions to a two dimensional modified Dirac-Klein-Gordon system of equations, Comm. Math. Phys., Vol. 151, 1993, pp. 67-87. | MR 1201656 | Zbl 0765.35046
[33] , Global weak solutions for the 2 + 1 dimensional wave maps with small energy, preprint, 1995.
[34] , Global weak solutions for 1 + 2 dimensional wave maps into homogeneous spaces, Ann. IHP-Analyse non linéaire, to appear. | Numdam | Zbl 0997.58012