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ON SINGULARITY FOR THE m-HARMONIC FLOW (Theory of function spaces and related topics)

Misawa, Masashi 京都大学

2023.05

概要

We study local regularity and singularity for the evolution of m-harmonic maps on ℝ[m] into a smooth compact Riemannian manifold, called m-harmonic flow. For any initial data of finite m-energy, the global existence of them-harmonic flow, which is regular except at most finitely many timespace points, is reported. The key ingredient is the uniform local regularity estimate for regular m-harmonic flows.

参考文献

[1] K.-C. Chang, Heat flow and boundary value problem for harmonic maps, Ann. Inst.

Henri Poincare, Anal. Non Lineaire 6, no. 5 (1989), 363-395.

[2] K.-C. Chang, W. -Y. Ding, R. Ye, Finite-time blow up of the heat flow of harmonic

maps from surfaces, J. Differential Geom. 36, no. 2 (1992), 507-515.

56

[3] C.-N. Chen, L. F. Cheung, Y. S. Choi, C. K. Law, On the blow-up of heat flow for

conformal 3-harmonic maps, Trans. AMS 354, no. 12, (2002) 5087-5110.

[4] H. J. Choe, Holder continuity of solutions of certain degenerate parabolic systems,

Nonlinear Anal. 8(3), (1992) 235-243.

[5] E. DiBenedetto, Degenerate Parabolic Equations,

Springer-Verlag. xv, 387 (1993).

Universitext, New York, NY:

[6] F. Duzaar, M. Fuchs, On removable singularities of p-harmonic maps, Ann. Inst.

Henri Poincare, Anal. Non Lineaire 7, no. 5, (1990) 385-405.

[7] F. Duzaar, G. Mingione, The p-harmonic approximation and the regularity of

p-harmonic maps, Cale. Var. Partial Differential Equations, 20, (2004) 235-256.

[8] J. Eells, J. H. Sampson, Harmonic mappings of Riemannian manifolds, Am. J. Math.

86 (1964), 109-169.

[9] A. Fardoun, R. Regbaoui, Heat flow for p-harmonic maps between compact Riemannian manifolds, Indiana Univ. Math. J. 51, no. 6, (2002), 1305-1320.

[10] R. Hamilton, Harmonic maps of manifolds with boundarym-harmonic flow, Leet.

Notes in Math. 471, Springer-Verlag, Berlin-New York, 1975. 593-631.

[11] N. Hungerbiihler, m-harmonic flow,

(1997), 593-631.

Ann. Scuola Norm. Sup. Pisa CI. Sci. 24

[12] C. Karim, M. Misawa, Gradient Holder regularity for nonlinear parabolic systems of

p-Laplacian type, Differential Integral Equations 29 (2016), no. 3-4, 201-228.

[13] M. Misawa, Local Holder regularity of gradients for evolutional p- Laplacian systems,

Ann. Mat. Pura Appl. {IV) 181, (2002) 389-405.

[14] M. Misawa, Existence and regularity results for the gradient flow for p-harmonic

maps, Electron J. Differ. Equ. 36 (1998), 1-17.

[15] M. Misawa, Regularity for the evolution of p-harmonic maps, J. Differential Equations 264, (2018) 1716-1749.

[16] M. Misawa, Local regularity and compactness for the p-harmonic map heat flows,

Adv. Cale. Var. (2017), DOI: 10.1515/acv-2016-0064.

[17] M. Misawa, Global existence and partial regularity for the p-harmonic flow, Cale.

Var. 58:54 (2019), DOI: 10.1515/acv-2016-0064.

[18] R .. Schoen, Analytic aspects of the harmonic map problem, Seminar on Nonlinear

Partial Differential Equations (S. S. Chern editor), MSRI Publications 2, (1984),

321-358, Springer-Verlag, New-York.

[19] M. Struwe, On the evolution of harmonic maps of Riemannian surfaces, Comment.

Math. Helv. 60, (1985), no.4, 558-581.

[20] M. Struwe, On the evolution of harmonic maps in higher dimensions, J. Differential

Geometry 28, (1988) 485-502.

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