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Gradient estimates for some diffusion semigroups
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  • Published: April 2002

Gradient estimates for some diffusion semigroups

  • Jean Picard1 

Probability Theory and Related Fields volume 122, pages 593–612 (2002)Cite this article

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Abstract

 Consider the semigroup $P_t$ of an elliptic diffusion; we describe a simple stochastic method providing gradient estimates on $P_tf$. If $N$ is a manifold endowed with a connection, the method can also be applied to the associated nonlinear semigroup $Q_t$ acting on $N$-valued maps. With a localization technique, we deduce gradient estimates for real harmonic functions or $N$-valued harmonic maps. Moreover, the results are extended to a class of hypoelliptic diffusions.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées (CNRS-UMR 6620), Université Blaise Pascal, 63177 Aubière Cedex, France. email:Jean.Picard@math.univ-bpclermont.fr, , , , , , FR

    Jean Picard

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  1. Jean Picard
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Received: 31 July 2000 / Revised version: 20 September 2001 / Published online: 15 March 2002

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Cite this article

Picard, J. Gradient estimates for some diffusion semigroups. Probab Theory Relat Fields 122, 593–612 (2002). https://doi.org/10.1007/s004400100185

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  • Issue Date: April 2002

  • DOI: https://doi.org/10.1007/s004400100185

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Keywords

  • Manifold
  • Harmonic Function
  • Localization Technique
  • Stochastic Method
  • Nonlinear Semigroup
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