Partial Regularity Results Up to the Boundary for Harmonic Maps Into a Finsler Manifold

Tachikawa, Atsushi

doi:10.1016/j.anihpc.2009.05.001

Tachikawa, Atsushi

Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1953-1970.

MR Zbl

DOI : 10.1016/j.anihpc.2009.05.001

@article{AIHPC_2009__26_5_1953_0,
     author = {Tachikawa, Atsushi},
     title = {Partial {Regularity} {Results} {Up} to the {Boundary} for {Harmonic} {Maps} {Into} a {Finsler} {Manifold}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1953--1970},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.05.001},
     mrnumber = {2566717},
     zbl = {1171.49028},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.05.001/}
}

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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, Tome 26 (2009) no. 5, pp. 1953-1970. doi : 10.1016/j.anihpc.2009.05.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.05.001/

Bibliographie
Cité par

[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. | MR | Zbl

[2] Bellettini G., Paolini M., Anisotropic Motion by Mean Curvature in the Context of Finsler Geometry, Hokkaido Math. J. 25 (1996) 537-566. | MR | Zbl

[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. | MR | Zbl

[4] Campanato S., A Maximum Principle for Non-Linear Elliptic Systems: Boundary Fundamental Estimates, Adv. Math. 66 (1987) 291-317. | MR | Zbl

[5] Centore P., Finsler Laplacians and Minimal-Energy Maps, Internat. J. Math. 11 (2000) 1-13. | MR | Zbl

[6] Eells J., Sampson J., Harmonic Mappings of Riemannian Manifolds, Amer. J. Math. 86 (1964) 109-160. | MR | Zbl

[7] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud., vol. 105, Princeton Univ. Press, 1983. | MR | Zbl

[8] Giaquinta M., Giusti E., On the Regularity of the Minima of Variational Integrals, Acta Math. 148 (1982) 31-46. | MR | Zbl

[9] Giaquinta M., Giusti E., Differentiability of Minima of Non-Differentiable Functionals, Invent. Math. 72 (1983) 285-298. | MR | Zbl

[10] Giaquinta M., Giusti E., The Singular Set of the Minima of Certain Quadratic Functionals, Ann. Sc. Norm. Super. Pisa 9 (1984) 45-55. | Numdam | MR | Zbl

[11] Giaquinta M., Hildebrandt S., A Priori Estimates for Harmonic Mappings, J. Reine Angew. Math. 336 (1982) 124-164. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[14] Giusti E., Direct Method in the Calculus of Variations, World Scientific, 2003. | MR | Zbl

[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. | MR | Zbl

[16] Jost J., Meier M., Boundary Regularity for Minima of Certain Quadratic Functionals, Math. Ann. 262 (1983) 549-561. | MR | Zbl

[17] Marcus M., Mizel V., Continuity of Certain Nemitsky Operators on Sobolev Spaces and the Chain Rule, J. Anal. Math. 28 (1975) 303-334. | MR | Zbl

[18] Mo X., Harmonic Maps From Finsler Spaces, Illinois J. Math. 45 (2001) 1331-1345. | MR | Zbl

[19] Mo X., Yang Y., The Existence of Harmonic Maps From Finsler Manifolds to Riemannian Manifolds, Sci. China Ser. A 48 (2005) 115-130. | MR | Zbl

[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. | MR | Zbl

[21] Nishikawa S., Harmonic Maps of Finsler Manifolds, in: Topics in Differential Geometry, Printing House of the Romanian Academy, 2008. | MR | Zbl

[22] Schoen R., Uhlenbeck K., A Regularity Theory for Harmonic Maps, J. Differential Geom. 17 (2) (1982) 307-335. | MR | Zbl

[23] Schoen R., Uhlenbeck K., Boundary Regularity and the Dirichlet Problem for Harmonic Maps, J. Differential Geom. 18 (2) (1983) 253-268. | MR | Zbl

[24] Shen Y.-B., Zhang Y., Second Variation of Harmonic Maps Between Finsler Manifolds, Sci. China Ser. A 47 (2004) 39-51. | MR

[25] Tachikawa A., A Partial Regularity Result for Harmonic Maps Into a Finsler Manifold, Calc. Var. Partial Differential Equations 15 (2003) 217-224, Calc. Var. Partial Differential Equations 15 (2003) 225-226, (Erratum). | Zbl

[26] Von Der Mosel H., Winklmann S., On Weakly Harmonic Maps From Finsler to Riemannian Manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (1) (2009) 39-57. | Numdam | MR | Zbl

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