Partial regularity for biharmonic maps, revisited

1. Adams, D.R., Frazier, M.: Composition operators on potential spaces. Proc. Am. Math. Soc. 114(1), 155–165 (1992)

   Article  MathSciNet  MATH  Google Scholar 

2. Angelsberg, G.: A monotonicity formula for stationary biharmonic maps. Math. Z. 252(2), 287–293 (2006)

   Article  MathSciNet  MATH  Google Scholar 

3. Chang, S.-Y.A., Wang, L., Yang, P.C.: A regularity theory of biharmonic maps. Commun. Pure Appl. Math. 52, 1113–1137 (1999)

   Article  MathSciNet  MATH  Google Scholar 

4. Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, vol. 105. Princeton University Press, Princeton (1983)

   Google Scholar 

5. Hélein, F.: Harmonic maps, conservation laws and moving frames, Cambridge Tracts in Mathematics, vol. 150. Cambridge University Press, Cambridge (2002)

   Google Scholar 

6. Lamm, T., Rivière, T.: Conservation laws for fourth order systems in four dimensions (2006, preprint) arXiv:math/0607484v1

7. Meyer, Y., Rivière, T.: A partial regularity result for a class of stationary Yang-Mills fields in high dimension. Rev. Mat. Iberoamericana 19(1), 195–219 (2003)

   MathSciNet  MATH  Google Scholar 

8. Rivière, T.: Conservation laws for conformally invariant variational problems. Invent. Math. 168(1), 1–22 (2007)

   Article  MathSciNet  MATH  Google Scholar 

9. Rivière, T., Struwe, M.: Partial regularity for harmonic maps, and related problems. Commun. Pure Appl. Math. (to appear)

10. Strzelecki, P.: On biharmonic maps and their generalizations. Calc. Var. Partial Differ. Equ. 18(4), 401–432 (2003)

    Article  MathSciNet  MATH  Google Scholar 

11. Strzelecki, P.: Gagliardo-Nirenberg inequalities with a BMO term. Bull. Lond. Math. Soc. 38(2), 294–300 (2006)

    Article  MathSciNet  MATH  Google Scholar 

12. Tao, T., Tian, G.: A singularity removal theorem for Yang-Mills fields in higher dimensions. J. Am. Math. Soc. 17(3), 557–593 (2004)

    Article  MathSciNet  MATH  Google Scholar 

13. Uhlenbeck, K.K.: Connections with L ^p bounds on curvature. Commun. Math. Phys. 83, 31–42 (1982)

    Article  MathSciNet  MATH  Google Scholar 

14. Wang, C.: Stationary biharmonic maps from \({\mathbb{R}^m}\) into a Riemannian manifold. Commun. Pure Appl. Math. 57(4), 419– (2004)

    Article  MATH  Google Scholar 

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