@article{AIHPC_2009__26_4_1387_0, 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}, volume = {26}, number = {4}, year = {2009}, doi = {10.1016/j.anihpc.2008.10.008}, mrnumber = {2542730}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.008/} }
TY - JOUR AU - Goldstein, Paweł AU - Strzelecki, Paweł AU - Zatorska-Goldstein, Anna TI - On Polyharmonic Maps Into Spheres in the Critical Dimension JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 1387 EP - 1405 VL - 26 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.008/ DO - 10.1016/j.anihpc.2008.10.008 LA - en ID - AIHPC_2009__26_4_1387_0 ER -
%0 Journal Article %A Goldstein, Paweł %A Strzelecki, Paweł %A Zatorska-Goldstein, Anna %T On Polyharmonic Maps Into Spheres in the Critical Dimension %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1387-1405 %V 26 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.008/ %R 10.1016/j.anihpc.2008.10.008 %G en %F AIHPC_2009__26_4_1387_0
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. http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.008/
[1] 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] On the Singular Set of Stationary Harmonic Maps, Manuscripta Math. 78 (1993) 417-443. | MR | Zbl
,[4] A Regularity Theory of Biharmonic Maps, Comm. Pure Appl. Math. 52 (1999) 1113-1137. | MR | Zbl
, , ,[5] Compensated Compactness and Hardy Spaces, J. Math. Pures Appl. 72 (1993) 247-286. | MR | Zbl
, , , ,[6] Partial Regularity for Stationary Harmonic Maps Into Spheres, Arch. Ration. Mech. Anal. 116 (1991) 101-113. | MR | Zbl
,[7] A Discontinuous Solution of a Mildly Nonlinear Elliptic System, Math. Z. 134 (1973) 229-230. | MR | Zbl
,[8] 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] Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton University Press, Princeton, NJ, 1983. | MR | Zbl
,[11] Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224, second ed., Springer-Verlag, Berlin, 1983. | MR | Zbl
, ,[12] Sobolev Met Poincaré, Mem. Amer. Math. Soc. 145 (688) (2000), x+101 pp. | MR | Zbl
, ,[13] Subelliptic P-Harmonic Maps Into Spheres and the Ghost of Hardy Spaces, Math. Ann. 312 (2) (1998) 341-362. | MR | Zbl
, ,[14] Harmonic Maps, Conservation Laws and Moving Frames, Cambridge Tracts in Mathematics, vol. 150, Cambridge University Press, Cambridge, 2002. | MR | Zbl
,[15] Conservation Laws for Fourth Order Systems in Four Dimensions, Comm. Partial Differential Equations 33 (2008) 245-262. | MR | Zbl
, ,[16] 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] Everywhere Discontinuous Harmonic Maps Into Spheres, Acta Math. 175 (2) (1995) 197-226. | MR | Zbl
,[19] Conservation Laws for Conformally Invariant Variational Problems, Invent. Math. 168 (2007) 1-22. | MR | Zbl
,[20] Partial Regularity for Harmonic Maps, and Related Problems, Comm. Pure Appl. Math. 61 (2008) 451-463. | MR | Zbl
, ,[21] 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] Dimension Reduction for the Singular Set of Biharmonic Maps, Adv. Calc. Var. 1 (1) (2008) 53-91. | MR | Zbl
,[23] Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl
,[24] Hardy Space Estimates for Higher-Order Differential Operators, Indiana Univ. Math. J. 50 (2001) 1447-1461. | MR | Zbl
,[25] On Biharmonic Maps and Their Generalizations, Calc. Var. Partial Differential Equations 18 (2003) 401-432. | MR | Zbl
,[26] Connections With Bounds on Curvature, Comm. Math. Phys. 83 (1982) 31-42. | MR | Zbl
,[27] Biharmonic Maps From Into a Riemannian Manifold, Math. Z. 247 (1) (2004) 65-87. | MR | Zbl
,Cité par Sources :