@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}, publisher = {Gauthier-Villars}, volume = {15}, number = {6}, year = {1998}, mrnumber = {1650966}, zbl = {0924.58011}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 15 (1998) no. 6, pp. 725-754. http://archive.numdam.org/item/AIHPC_1998__15_6_725_0/
[1] Weak limits of solutions to the steady incompressible
and ,two-dimensional Euler equations in a bounded domain, Asympt. Anal., Vol. 8, 1994, pp. 277-291. | MR | Zbl
[2] Weak convergence of Palais-Smale sequences for some critical functionals, Calc. Var., Vol. 1, 1993, pp. 267-310. | MR | Zbl
,[3] On the singular set of stationary harmonic maps, manusc. math., Vol. 78, 1993, pp. 417-443. | MR | Zbl
,[4] Sistemi ellittiche del secondo ordine e spazi L2.λ, Ann. Mat. Pura Appl., Vol. 69, 1965, pp. 321-380. | MR | Zbl
,[5] On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1041-1091. | MR | Zbl
and ,[6] Compensated compactness and Hardy spaces, J. Math. Pures Appl., Vol. 72, 1993, pp. 247-286. | MR | Zbl
, , and ,[7] Reduced Hausdorff dimension and concentration cancellation for two-dimensional incompressible flows, J. Amer. Math. Soc., Vol. 1. 1988, pp. 59-95. | MR | Zbl
and ,[8] Partial regularity for stationary harmonic maps into spheres, Arch. Rat. Mech. Anal., Vol. 116, 1991, 101-113. | MR | Zbl
,[9] Hp spaces of several variables, Acta Math., Vol. 129, 1972, pp. 137-193. | MR | Zbl
and ,[10] Capacity methods in the theory of partial differential equations, Jahresb. Dt. Math. Ver., Vol. 84, 1982, pp. 1-44. | MR | Zbl
,[11] Global weak solutions of the wave map system to compact homogeneous spaces, manuscripta math., Vol. 91, 1996, pp. 525-533. | MR | Zbl
,[12] Weak convergence of wave maps from (2+1) dimensional Minkowski space to Riemannian manifolds, Invent. Math., Vol. 130, 1997, pp. 589-617. | MR | Zbl
, and ,[13] Introduction to regularity theory for nonlinear elliptic systems, Lectures in Mathematics, Birkhäuser, 1993. | MR | Zbl
,[14] A local version of the Hardy space, Duke Math. J., Vol. 46, 1979, pp. 27-42. | MR | Zbl
,[15] Elementare Bemerkung zur isoperimetrischen Ungleichung im R3, Math. Z., Vol. 132, 1973, pp. 319-322. | MR | Zbl
,[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 | Zbl
,[17] Space-time estimates for null forms and the local existence theorem, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 1221-1268. | MR | Zbl
and ,[18] Smoothing estimates for null forms and applications, Int. Math. Res. Not., Vol. 4, 1994, pp. 383-389. | MR | Zbl
and ,[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 | Zbl
,[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 | Zbl
,[21] Global existence of wave maps in 1+2 dimensions for finite energy data, Top. Methods Nonlinear Analysis, Vol. 7, 1996, pp. 245-259. | MR | Zbl
and ,[22] Harmonic maps on planar lattices, Ann. SNS Pisa, to appear. | Numdam
, and ,[23] Spatially discrete wave maps on (1+2)-dimensional space-time, Top. Methods Nonlinear Analysis, to appear. | Zbl
and ,[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 | Zbl
,[25] Weak solutions and development of singularities in the SU (2) σ-model, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 459-469. | MR | Zbl
,[26] On the Cauchy problem for equivariant wave maps, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 947-971. | MR | Zbl
and ,[27] Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970. | MR | Zbl
,[28] Harmonic analysis, Princeton Univ. Press, 1993. | MR | Zbl
,[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 | Zbl
,[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 | Zbl
,[31] An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl., Vol. 26, 1969, pp. 318-344. | MR | Zbl
,[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 | Zbl
,[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
,