An Optimal Partial Regularity Result for Minimizers of an Intrinsically Defined Second-Order Functional
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, p. 1585-1605
@article{AIHPC_2009__26_5_1585_0,
     author = {Scheven, Christoph},
     title = {An Optimal Partial Regularity Result for Minimizers of an Intrinsically Defined Second-Order Functional},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     pages = {1585-1605},
     doi = {10.1016/j.anihpc.2008.07.002},
     zbl = {pre05612918},
     mrnumber = {2566701},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_5_1585_0}
}
Scheven, Christoph. An Optimal Partial Regularity Result for Minimizers of an Intrinsically Defined Second-Order Functional. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1585-1605. doi : 10.1016/j.anihpc.2008.07.002. http://www.numdam.org/item/AIHPC_2009__26_5_1585_0/

[1] Adams D., A Note on Riesz Potentials, Duke Math. J. 42 (1975) 765-778. | MR 458158 | Zbl 0336.46038

[2] Avellaneda M., Lin F. H., Fonctions Quasi Affines Et Minimisation De u p , C. R. Acad. Sci. Paris Sér. I 306 (1988) 355-358. | MR 934618

[3] Chang A., Wang L., Yang P., A Regularity Theory of Biharmonic Maps, Comm. Pure Appl. Math. 52 (9) (1999) 1113-1137. | MR 1692148 | Zbl 0953.58013

[4] A. Gastel, C. Scheven, Regularity of polyharmonic maps in the critical dimension, submitted for publication. | Zbl pre05606319

[5] Hardy G., Littlewood J., Pólya G., Inequalities, Cambridge University Press, 1964. | JFM 60.0169.01 | Zbl 0047.05302

[6] Kobayashi S., Nomizu K., Foundations of Differential Geometry II, Interscience Publishers, New York, 1969. | Zbl 0175.48504

[7] Mattila P., Geometry of Sets and Measures in Euclidean Spaces - Fractals and Rectifiability, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, 1995. | MR 1333890 | Zbl 0819.28004

[8] Montaldo S., Oniciuc C., A Short Survey on Biharmonic Maps Between Riemannian Manifolds, Rev. Un. Mat. Argentina 47 (2006) 1-22. | MR 2301373 | Zbl 1140.58004

[9] Moser R., The Blow-Up Behavior of the Biharmonic Map Heat Flow in Four Dimensions, IMRP Int. Math. Res. Pap. 2005 (2005) 351-402. | MR 2204844 | Zbl 1124.53028

[10] R. Moser, A variational problem pertaining to biharmonic maps, preprint. | MR 2450176 | Zbl 1154.58007

[11] Simon L., Lectures on Geometric Measure Theory, Proc. of Centre for Math. Anal., vol. 3, Australian National Univ., 1983. | MR 756417 | Zbl 0546.49019

[12] Schoen R., Analytic Aspects of the Harmonic Map Problem, in: Chern S. S. (Ed.), Seminar on Nonlinear Partial Differential Equations, Springer, 1984, pp. 321-358. | MR 765241 | Zbl 0551.58011

[13] Scheven C., Dimension Reduction for the Singular Set of Biharmonic Maps, Adv. Calc. Var. 1 (2008) 53-91. | MR 2402212 | Zbl 1152.58011

[14] Strzelecki P., On Biharmonic Maps and Their Generalizations, Calc. Var. 18 (4) (2003) 401-432. | MR 2020368 | Zbl 1106.35021

[15] Struwe M., Partial Regularity for Biharmonic Maps, revisited, Calc. Var. 33 (2) (2008) 249-262. | MR 2413109 | Zbl 1151.58011

[16] Tao T., Tian G., A Singularity Removal Theorem for Yang-Mills Fields in Higher Dimensions, J. Amer. Math. Soc. 17 (2004) 557-593. | MR 2053951 | Zbl 1086.53043

[17] Wang C., Remarks on Biharmonic Maps Into Spheres, Calc. Var. 21 (3) (2004) 221-242. | MR 2094320 | Zbl 1060.58011

[18] Wang C., Biharmonic Maps From R 4 Into a Riemannian Manifold, Math. Z. 247 (1) (2004) 65-87. | MR 2054520 | Zbl 1064.58016

[19] Wang C., Stationary Biharmonic Maps From R m Into a Riemannian Manifold, Comm. Pure Appl. Math. 57 (4) (2004) 419-444. | MR 2026177 | Zbl 1055.58008

[20] Ziemer W., Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation, Graduate Texts in Mathematics, vol. 120, Springer, New York, 1989. | MR 1014685 | Zbl 0692.46022