Freire, Alexandre 1 ; Müller, Stefan 2 ; Struwe, Michael 3
@article{AIHPC_1998__15_6_725_0,
author = {Freire, Alexandre and M\"uller, Stefan and Struwe, Michael},
title = {Weak compactness of wave maps and harmonic maps},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {725--754},
year = {1998},
publisher = {Gauthier-Villars},
volume = {15},
number = {6},
mrnumber = {1650966},
zbl = {0924.58011},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1998__15_6_725_0/}
}
TY - JOUR AU - Freire, Alexandre AU - Müller, Stefan AU - Struwe, Michael TI - Weak compactness of wave maps and harmonic maps JO - Annales de l'I.H.P. Analyse non linéaire PY - 1998 SP - 725 EP - 754 VL - 15 IS - 6 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1998__15_6_725_0/ LA - en ID - AIHPC_1998__15_6_725_0 ER -
%0 Journal Article %A Freire, Alexandre %A Müller, Stefan %A Struwe, Michael %T Weak compactness of wave maps and harmonic maps %J Annales de l'I.H.P. Analyse non linéaire %D 1998 %P 725-754 %V 15 %N 6 %I Gauthier-Villars %U https://www.numdam.org/item/AIHPC_1998__15_6_725_0/ %G en %F AIHPC_1998__15_6_725_0
Freire, Alexandre; Müller, Stefan; Struwe, Michael. Weak compactness of wave maps and harmonic maps. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 6, pp. 725-754. https://www.numdam.org/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. | Zbl | MR
[2] , Weak convergence of Palais-Smale sequences for some critical functionals, Calc. Var., Vol. 1, 1993, pp. 267-310. | Zbl | MR
[3] , On the singular set of stationary harmonic maps, manusc. math., Vol. 78, 1993, pp. 417-443. | Zbl | MR
[4] , Sistemi ellittiche del secondo ordine e spazi L2.λ, Ann. Mat. Pura Appl., Vol. 69, 1965, pp. 321-380. | Zbl | MR
[5] and , On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1041-1091. | Zbl | MR
[6] , , and , Compensated compactness and Hardy spaces, J. Math. Pures Appl., Vol. 72, 1993, pp. 247-286. | Zbl | MR
[7] and , Reduced Hausdorff dimension and concentration cancellation for two-dimensional incompressible flows, J. Amer. Math. Soc., Vol. 1. 1988, pp. 59-95. | Zbl | MR
[8] , Partial regularity for stationary harmonic maps into spheres, Arch. Rat. Mech. Anal., Vol. 116, 1991, 101-113. | Zbl | MR
[9] and , Hp spaces of several variables, Acta Math., Vol. 129, 1972, pp. 137-193. | Zbl | MR
[10] , Capacity methods in the theory of partial differential equations, Jahresb. Dt. Math. Ver., Vol. 84, 1982, pp. 1-44. | Zbl | MR
[11] , Global weak solutions of the wave map system to compact homogeneous spaces, manuscripta math., Vol. 91, 1996, pp. 525-533. | Zbl | MR
[12] , and , Weak convergence of wave maps from (2+1) dimensional Minkowski space to Riemannian manifolds, Invent. Math., Vol. 130, 1997, pp. 589-617. | Zbl | MR
[13] , Introduction to regularity theory for nonlinear elliptic systems, Lectures in Mathematics, Birkhäuser, 1993. | Zbl | MR
[14] , A local version of the Hardy space, Duke Math. J., Vol. 46, 1979, pp. 27-42. | Zbl | MR
[15] , Elementare Bemerkung zur isoperimetrischen Ungleichung im R3, Math. Z., Vol. 132, 1973, pp. 319-322. | Zbl | MR
[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. | Zbl | MR
[17] and , Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1221-1268. | Zbl | MR
[18] and , Smoothing estimates for null forms and applications, Int. Math. Res. Not., Vol. 4, 1994, pp. 383-389. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[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
[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. | Zbl | MR
[25] , Weak solutions and development of singularities in the SU (2) σ-model, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 459-469. | Zbl | MR
[26] and , On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 947-971. | Zbl | MR
[27] , Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970. | Zbl | MR
[28] , Harmonic analysis, Princeton Univ. Press, 1993. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[31] , An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl., Vol. 26, 1969, pp. 318-344. | Zbl | MR
[32] , Regularity of solutions to a two dimensional modified Dirac-Klein-Gordon system of equations, Comm. Math. Phys., Vol. 151, 1993, pp. 67-87. | Zbl | MR
[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. | Zbl | Numdam






