On Polyharmonic Maps Into Spheres in the Critical Dimension

Goldstein, Paweł; Strzelecki, Paweł; Zatorska-Goldstein, Anna

doi:10.1016/j.anihpc.2008.10.008

Goldstein, Paweł ; Strzelecki, Paweł ; Zatorska-Goldstein, Anna

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1387-1405.

DOI : 10.1016/j.anihpc.2008.10.008

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     author = {Goldstein, Pawe{\l} and Strzelecki, Pawe{\l} and Zatorska-Goldstein, Anna},
     title = {On {Polyharmonic} {Maps} {Into} {Spheres} in the {Critical} {Dimension}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1387--1405},
     publisher = {Elsevier},
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     year = {2009},
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}

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Goldstein, Paweł; Strzelecki, Paweł; Zatorska-Goldstein, Anna. On Polyharmonic Maps Into Spheres in the Critical Dimension. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1387-1405. doi : 10.1016/j.anihpc.2008.10.008. https://www.numdam.org/articles/10.1016/j.anihpc.2008.10.008/

Bibliographie
Cité par

[1] Adams R. A., Sobolev Spaces, Pure and Applied Mathematics, vol. 65, Academic Press, New York-London, 1975. | MR | Zbl

[2] G. Angelsberg, D. Pumberger, A regularity result for polyharmonic maps with higher integrability, Preprint. | MR | Zbl

[3] Bethuel F., On the Singular Set of Stationary Harmonic Maps, Manuscripta Math. 78 (1993) 417-443. | MR | Zbl

[4] Chang S.-Y. A., Wang L., Yang P., A Regularity Theory of Biharmonic Maps, Comm. Pure Appl. Math. 52 (1999) 1113-1137. | MR | Zbl

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

[6] Evans L. C., Partial Regularity for Stationary Harmonic Maps Into Spheres, Arch. Ration. Mech. Anal. 116 (1991) 101-113. | MR | Zbl

[7] Frehse J., A Discontinuous Solution of a Mildly Nonlinear Elliptic System, Math. Z. 134 (1973) 229-230. | MR | Zbl

[8] Gastel A., The Extrinsic Polyharmonic Map Heat Flow in the Critical Dimension, Adv. Geom. 6 (2006) 501-521. | MR | Zbl

[9] A. Gastel, C. Scheven, Regularity of polyharmonic maps in the critical dimension, Commun. Anal. Geom., in press. | MR

[10] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, NJ, 1983. | MR | Zbl

[11] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, second ed., Springer-Verlag, Berlin, 1983. | MR | Zbl

[12] Hajłasz P., Koskela P., Sobolev Met Poincaré, Mem. Amer. Math. Soc. 145 (688) (2000), x+101 pp. | MR | Zbl

[13] Hajłasz P., Strzelecki P., Subelliptic P-Harmonic Maps Into Spheres and the Ghost of Hardy Spaces, Math. Ann. 312 (2) (1998) 341-362. | MR | Zbl

[14] Hélein F., Harmonic Maps, Conservation Laws and Moving Frames, Cambridge Tracts in Mathematics, vol. 150, Cambridge University Press, Cambridge, 2002. | MR | Zbl

[15] Lamm T., Rivière T., Conservation Laws for Fourth Order Systems in Four Dimensions, Comm. Partial Differential Equations 33 (2008) 245-262. | MR | Zbl

[16] Meyer Y., Rivière T., A Partial Regularity Result for a Class of Stationary Yang-Mills Fields in High Dimension, Rev. Mat. Iberoamericana 19 (1) (2003) 195-219. | MR | Zbl

[17] D. Pumberger, Regularity results for stationary harmonic and J-holomorphic maps, Preprint, ETH Zuerich, 2004.

[18] Rivière T., Everywhere Discontinuous Harmonic Maps Into Spheres, Acta Math. 175 (2) (1995) 197-226. | MR | Zbl

[19] Rivière T., Conservation Laws for Conformally Invariant Variational Problems, Invent. Math. 168 (2007) 1-22. | MR | Zbl

[20] Rivière T., Struwe M., Partial Regularity for Harmonic Maps, and Related Problems, Comm. Pure Appl. Math. 61 (2008) 451-463. | MR | Zbl

[21] Rivière T., Strzelecki P., A Sharp Nonlinear Gagliardo-Nirenberg-Type Estimate and Applications to the Regularity of Elliptic Systems, Comm. Partial Differential Equations 30 (2005) 589-604. | MR | Zbl

[22] Scheven Ch., Dimension Reduction for the Singular Set of Biharmonic Maps, Adv. Calc. Var. 1 (1) (2008) 53-91. | MR | Zbl

[23] Stein E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl

[24] Strzelecki P., Hardy Space Estimates for Higher-Order Differential Operators, Indiana Univ. Math. J. 50 (2001) 1447-1461. | MR | Zbl

[25] Strzelecki P., On Biharmonic Maps and Their Generalizations, Calc. Var. Partial Differential Equations 18 (2003) 401-432. | MR | Zbl

[26] Uhlenbeck K., Connections With $L^{p}$ Bounds on Curvature, Comm. Math. Phys. 83 (1982) 31-42. | MR | Zbl

[27] Wang Ch., Biharmonic Maps From $R^{4}$ Into a Riemannian Manifold, Math. Z. 247 (1) (2004) 65-87. | MR | Zbl

Guo, Changyu; Qi, Wenjuan Sharp Morrey Regularity for an Even Order Elliptic System, Acta Mathematica Sinica, English Series, Volume 41 (2025) no. 3, p. 925 | DOI:10.1007/s10114-025-3353-9
Guo, Changyu; Xiang, Changlin; Zheng, Gaofeng Refined conservation law for an even order elliptic system with antisymmetric potential, Acta Mathematica Scientia, Volume 44 (2024) no. 6, p. 2111 | DOI:10.1007/s10473-024-0604-2
Guo, Chang-Yu; Xiang, Chang-Lin; Zheng, Gao-Feng L regularity theory for even order elliptic systems with antisymmetric first order potentials, Journal de Mathématiques Pures et Appliquées, Volume 165 (2022), p. 286 | DOI:10.1016/j.matpur.2022.07.010
Branding, Volker A structure theorem for polyharmonic maps between Riemannian manifolds, Journal of Differential Equations, Volume 273 (2021), p. 14 | DOI:10.1016/j.jde.2020.11.046
Misawa, Masashi; Nakauchi, Nobumitsu Regularity of the m-symphonic map, Partial Differential Equations and Applications, Volume 2 (2021) no. 2 | DOI:10.1007/s42985-021-00074-y
Guo, Chang-Yu; Xiang, Chang-Lin Regularity of weak solutions to higher order elliptic systems in critical dimensions, Transactions of the American Mathematical Society, Volume 374 (2021) no. 5, p. 3579 | DOI:10.1090/tran/8326
Guo, Chang‐Yu; Xiang, Chang‐Lin Regularity of solutions for a fourth‐order elliptic system via Conservation law, Journal of the London Mathematical Society, Volume 101 (2020) no. 3, p. 907 | DOI:10.1112/jlms.12289
Convent, Alexandra; Van Schaftingen, Jean Higher order intrinsic weak differentiability and Sobolev spaces between manifolds, Advances in Calculus of Variations, Volume 12 (2019) no. 3, p. 303 | DOI:10.1515/acv-2017-0008
Ai, Wanjun; Yin, Hao Neck analysis of extrinsic polyharmonic maps, Annals of Global Analysis and Geometry, Volume 52 (2017) no. 2, p. 129 | DOI:10.1007/s10455-017-9551-7
Blatt, Simon Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane–Emden equation, Journal of Differential Equations, Volume 262 (2017) no. 12, p. 5691 | DOI:10.1016/j.jde.2017.01.025
Zheng, Shenzhou A compactness result for polyharmonic maps in the critical dimension, Czechoslovak Mathematical Journal, Volume 66 (2016) no. 1, p. 137 | DOI:10.1007/s10587-016-0246-1
Cooper, Matthew K. Critical O(d)-equivariant biharmonic maps, Calculus of Variations and Partial Differential Equations, Volume 54 (2015) no. 3, p. 2895 | DOI:10.1007/s00526-015-0888-0
Schikorra, Armin Regularity of n/2-harmonic maps into spheres, Journal of Differential Equations, Volume 252 (2012) no. 2, p. 1862 | DOI:10.1016/j.jde.2011.08.021
Huang, Tao; Wang, Changyou Well-posedness for the heat flow of polyharmonic maps with rough initial data, Advances in Calculus of Variations, Volume 4 (2011) no. 2 | DOI:10.1515/acv.2010.025

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