A compactness theorem of $n$-harmonic maps

Wang, Chang You

doi:10.1016/j.anihpc.2004.10.007

A compactness theorem of

n

-harmonic maps

Wang, Chang You

Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 509-519.

Zbl

DOI : 10.1016/j.anihpc.2004.10.007

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     author = {Wang, Chang You},
     title = {A compactness theorem of $n$-harmonic maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {509--519},
     publisher = {Elsevier},
     volume = {22},
     number = {4},
     year = {2005},
     doi = {10.1016/j.anihpc.2004.10.007},
     zbl = {02191852},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.007/}
}

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Wang, Chang You. A compactness theorem of $n$-harmonic maps. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 509-519. doi : 10.1016/j.anihpc.2004.10.007. http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.007/

Bibliographie
Cité par

[1] Bethuel F., Weak limits of Palais-Smale sequences for a class of critical functionals, Calc. Var. Partial Differential Equations 1 (3) (1993) 267-310. | MR | Zbl

[2] Bethuel F., On the singular set of stationary harmonic maps, Manuscripta Math. 78 (1993) 417-443. | MR | Zbl

[3] Chen Y.M., The weak solutions to the evolution problems of harmonic maps, Math. Z. 201 (1) (1989) 69-74. | MR | Zbl

[4] Coifman R., Lions P., Meyer Y., Semmes S., Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993) 247-286. | MR | Zbl

[5] Evans L.C., Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal. 116 (1991) 101-113. | MR | Zbl

[6] Evans L.C., Weak Convergence Methods for Nonlinear Partial Differential Equations, CBMS Regional Conf. Ser. in Math., vol. 74, 1990. | MR | Zbl

[7] Evans L.C., Gariepy R., Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1992. | MR | Zbl

[8] Fefferman C., Stein E., $H^{p}$ spaces of several variables, Acta Math. 129 (1972) 137-193. | MR | Zbl

[9] Freire A., Müller S., Struwe M., Weak convergence of wave maps from (1+2)-dimensional Minkowski space to Riemannian manifolds, Invent. Math. 130 (3) (1997) 589-617. | MR | Zbl

[10] Freire A., Müller S., Struwe M., Weak compactness of wave maps and harmonic maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (6) (1998) 725-754. | Numdam | MR | Zbl

[11] Fuchs M., The blow-up of p-harmonic maps, Manuscripta Math. 81 (1-2) (1993) 89-94. | MR | Zbl

[12] Hélein F., Regularite des applications faiblement harmoniques entre une surface et variete riemannienne, C. R. Acad. Sci. Paris 312 (1991) 591-596. | MR | Zbl

[13] Hardt R., Lin F.H., Mappings minimizing the $L^{p}$ norm of the gradient, Comm. Pure Appl. Math. 40 (5) (1987) 555-588. | MR | Zbl

[14] Hardt R., Lin F.H., Mou L., Strong convergence of p-harmonic mappings, in: Progress in Partial Differential Equations: The Metz Surveys, 3, Pitman Res. Notes Math. Ser., vol. 314, Longman Sci. Tech., Harlow, 1994, pp. 58-64. | MR | Zbl

[15] Hélein F., Harmonic Maps, Conservation Laws and Moving Frames, Cambridge Tracts in Math., vol. 150, Cambridge Univ. Press, Cambridge, 2002. | MR | Zbl

[16] Hungerbhler N., m-harmonic flow, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (4) (1997) 593-631, (1998). | Numdam | MR | Zbl

[17] Iwaniec T., Martin G., Quasiregular mappings in even dimensions, Acta Math. 170 (1) (1993) 29-81. | MR | Zbl

[18] John F., Nirenberg L., On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961) 415-426. | MR | Zbl

[19] Lions P.L., The concentration-compactness principle in the calculus of variations: the limit case, I, Rev. Mat. Iberoamericana 1 (1) (1985) 145-201. | MR | Zbl

[20] Lions P.L., The concentration-compactness principle in the calculus of variations: the limit case, II, Rev. Mat. Iberoamericana 1 (2) (1985) 45-121. | MR | Zbl

[21] Luckhaus S., Convergence of minimizers for the p-Dirichlet integral, Math. Z. 213 (3) (1993) 449-456. | MR | Zbl

[22] Sacks J., Uhlenbeck K., The existence of minimal immersions of 2-spheres, Ann. of Math. 113 (1981) 1-24. | MR | Zbl

[23] Schoen R., Uhlenbeck K., A regularity theory for harmonic maps, J. Differential Geom. 17 (2) (1982) 307-335. | MR | Zbl

[24] Shatah J., Weak solutions and development of singularities of the $SU (2)$ σ-model, Comm. Pure Appl. Math. 41 (4) (1988) 459-469. | Zbl

[25] Strzelecki P., Zatorska-Goldstein A., A compactness theorem for weak solutions of higher-dimensional H-systems, Duke Math. J. 121 (2) (2004) 269-284. | MR | Zbl

[26] Toro T., Wang C.Y., Compactness properties of weakly p-harmonic maps into homogeneous spaces, Indiana Univ. Math. J. 44 (1) (1995) 87-113. | MR | Zbl

[27] Uhlenbeck K., Connections with $L^{p}$ -bounds on curvature, Comm. Math. Phys. 83 (1982) 31-42. | MR | Zbl

[28] Wang C.Y., Bubble phenomena of certain Palais-Smale sequences from surfaces to general targets, Houston J. Math. 22 (3) (1996) 559-590. | MR | Zbl

[29] Wang C.Y., Stationary biharmonic maps from $R^{n}$ into a Riemannian manifold, Comm. Pure Appl. Math. LVII (2004) 0419-0444. | MR | Zbl

[30] Wang C.Y., Biharmonic maps from $R^{4}$ into a Riemannian manifold, Math. Z. 247 (1) (2004) 65-87. | MR | Zbl

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