Partial regularity results up to the boundary for harmonic maps into a Finsler manifold

Atsushi Tachikawa

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1953-1970
  • ISSN: 0294-1449

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Tachikawa, Atsushi. "Partial regularity results up to the boundary for harmonic maps into a Finsler manifold." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1953-1970. <http://eudml.org/doc/78920>.

@article{Tachikawa2009,
author = {Tachikawa, Atsushi},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {harmonic map; Finsler manifold; partial regularity},
language = {eng},
number = {5},
pages = {1953-1970},
publisher = {Elsevier},
title = {Partial regularity results up to the boundary for harmonic maps into a Finsler manifold},
url = {http://eudml.org/doc/78920},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Tachikawa, Atsushi
TI - Partial regularity results up to the boundary for harmonic maps into a Finsler manifold
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1953
EP - 1970
LA - eng
KW - harmonic map; Finsler manifold; partial regularity
UR - http://eudml.org/doc/78920
ER -

References

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  1. [1] Antonelli P.L., Ingarten R.S., Matsumoto M., The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers Group, 1993. Zbl0821.53001MR1273129
  2. [2] Bellettini G., Paolini M., Anisotropic motion by mean curvature in the context of Finsler geometry, Hokkaido Math. J.25 (1996) 537-566. Zbl0873.53011MR1416006
  3. [3] Campanato S., Elliptic systems with non-linearity q greater or equal to two. Regularity of the solution of the Dirichlet problem, Ann. Mat. Pura Appl.147 (1987) 117-150. Zbl0635.35038MR916705
  4. [4] Campanato S., A maximum principle for non-linear elliptic systems: Boundary fundamental estimates, Adv. Math.66 (1987) 291-317. Zbl0644.35042MR915857
  5. [5] Centore P., Finsler laplacians and minimal-energy maps, Internat. J. Math.11 (2000) 1-13. Zbl1110.58307MR1757888
  6. [6] Eells J., Sampson J., Harmonic mappings of Riemannian manifolds, Amer. J. Math.86 (1964) 109-160. Zbl0122.40102MR164306
  7. [7] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud., vol. 105, Princeton Univ. Press, 1983. Zbl0516.49003MR717034
  8. [8] Giaquinta M., Giusti E., On the regularity of the minima of variational integrals, Acta Math.148 (1982) 31-46. Zbl0494.49031MR666107
  9. [9] Giaquinta M., Giusti E., Differentiability of minima of non-differentiable functionals, Invent. Math.72 (1983) 285-298. Zbl0513.49003MR700772
  10. [10] Giaquinta M., Giusti E., The singular set of the minima of certain quadratic functionals, Ann. Sc. Norm. Super. Pisa9 (1984) 45-55. Zbl0543.49018MR752579
  11. [11] Giaquinta M., Hildebrandt S., A priori estimates for harmonic mappings, J. Reine Angew. Math.336 (1982) 124-164. Zbl0508.58015MR671325
  12. [12] Giaquinta M., Martinazzi L., An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs, Appunti. Sc. Norm. Super. Pisa (N. S.), vol. 2, Edizioni della Normale, Pisa, 2005. Zbl1093.35001MR2192611
  13. [13] Giaquinta M., Modica G., Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math.311/312 (1979) 145-169. Zbl0409.35015MR549962
  14. [14] Giusti E., Direct Method in the Calculus of Variations, World Scientific, 2003. Zbl1028.49001MR1962933
  15. [15] Hildebrandt S., Kaul H., Widman K.-O., An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math.138 (1–2) (1977) 1-16. Zbl0356.53015MR433502
  16. [16] Jost J., Meier M., Boundary regularity for minima of certain quadratic functionals, Math. Ann.262 (1983) 549-561. Zbl0488.49004MR696525
  17. [17] Marcus M., Mizel V., Continuity of certain Nemitsky operators on Sobolev spaces and the chain rule, J. Anal. Math.28 (1975) 303-334. Zbl0328.46028MR482444
  18. [18] Mo X., Harmonic maps from Finsler spaces, Illinois J. Math.45 (2001) 1331-1345. Zbl0996.53047MR1895460
  19. [19] Mo X., Yang Y., The existence of harmonic maps from Finsler manifolds to Riemannian manifolds, Sci. China Ser. A48 (2005) 115-130. Zbl1127.58011MR2156621
  20. [20] Nishikawa S., Harmonic maps in complex Finsler geometry. Variational problems in Riemannian geometry, in: Progr. Nonlinear Differential Equations Appl., vol. 59, Birkhäuser, Basel, 2004, pp. 113-132. Zbl1064.58015MR2076270
  21. [21] Nishikawa S., Harmonic maps of Finsler manifolds, in: Topics in Differential Geometry, Printing House of the Romanian Academy, 2008. Zbl1157.53032MR2484673
  22. [22] Schoen R., Uhlenbeck K., A regularity theory for harmonic maps, J. Differential Geom.17 (2) (1982) 307-335. Zbl0521.58021MR664498
  23. [23] Schoen R., Uhlenbeck K., Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom.18 (2) (1983) 253-268. Zbl0547.58020MR710054
  24. [24] Shen Y.-B., Zhang Y., Second variation of harmonic maps between Finsler manifolds, Sci. China Ser. A47 (2004) 39-51. MR2054666
  25. [25] Tachikawa A., A partial regularity result for harmonic maps into a Finsler manifold, Calc. Var. Partial Differential Equations15 (2003) 217-224, Calc. Var. Partial Differential Equations15 (2003) 225-226, (Erratum). Zbl1023.49032
  26. [26] von der Mosel H., Winklmann S., On weakly harmonic maps from Finsler to Riemannian manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire26 (1) (2009) 39-57. Zbl1166.53050MR2483812

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