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The p-Harmonic Heat Flow with Potential into Homogeneous Spaces

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Abstract

In this paper we prove the existence of global weak solutions of the p-harmonic flow with potential between Riemannian manifolds M and N for arbitrary initial data having finite p-energy in the case when the target N is a homogeneous space with a left invariant metric.

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References

  1. Fardoun A., Ratto. A., Harmonic maps with potential, Carc. Var., 1997, 5:183–197

    Article  MATH  MathSciNet  Google Scholar 

  2. Hungrbuhler N., Global weak solutions of the p-harmonic flow into homogeneous spaces, Indi. Univ. Math. J., 1996, 45(1):275–288

    Google Scholar 

  3. Héléin F., Régularte des applicationa faiblement harmoniques entre une surface et une variete Riemannienne, C R Acad. Sci. Paris, 1991, 312:591–596

    MATH  Google Scholar 

  4. Héléin F., Regularity of weakly harmonic maps from a surface into a manifold with symmetries, Manu. Math., 1991, 70:203–218

    MATH  Google Scholar 

  5. Liu X. G., A remark on p-harmonic heat flows, Chinese Sci. Bull., 1997, 42(6):441–444

    Article  MATH  MathSciNet  Google Scholar 

  6. Evans L. C., Weak convergence methods for nonlinear partial differential equations, in CBMS Reg. Conf. Ser. Math., 1990, 74

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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China

    Xian Gao Liu

  2. Institute of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China

    Sheng Hong Li

Authors
  1. Xian Gao Liu
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  2. Sheng Hong Li
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Correspondence to Xian Gao Liu.

Additional information

Project supportedpa rtially by STDF of Shanghai and NSF of China

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Liu, X.G., Li, S.H. The p-Harmonic Heat Flow with Potential into Homogeneous Spaces. Acta Math Sinica 18, 21–26 (2002). https://doi.org/10.1007/s101140000042

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  • DOI: https://doi.org/10.1007/s101140000042

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