TITLE

Improved regularity of harmonic map flows with Hölder continuous energy

AUTHOR(S)
Topping, Peter
PUB. DATE
September 2004
SOURCE
Calculus of Variations & Partial Differential Equations;Sep2004, Vol. 21 Issue 1, p47
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
For a smooth harmonic map flow u : M × [0, T) → N with blow-up as t ↑ T, it has been asked [6,5,7] whether the weak limit u(T) M → N is continuous. Recently, in [12], we showed that in general it need not be. Meanwhile, the energy function E(u(.)) [0, T) → R, being weakly positive, smooth and weakly decreasing, has a continuous extension to [0, T]. Here we show that if this extension is also Holder continuous, then the weak limit u(T) must also be Holder continuous.
ACCESSION #
13918440

 

Related Articles

  • A New One-Step Iterative Process for Common Fixed Points in Banach Spaces. Abbas, Mujahid; Khan, Safeer Hussain; Jong Kyu Kim // Journal of Inequalities & Applications;2008, Vol. 2008, p1 

    The article focuses on the use of a new one-step iterative process to approximate the common fixed points of asymptotically nonexpansive mappings through some weak and strong convergence theorems in Banach spaces. This process is computationally simpler than the Ishikawa-type two-step iterative...

  • A new look at some classical theorems on continuous functions on normal spaces. Gutiérrez García, J.; Kubiak, T. // Acta Mathematica Hungarica;Jun2008, Vol. 119 Issue 4, p333 

    A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker. Our insertion lemma also provides purely...

  • Harmonic Properties of Gauss Mappings in H3. Masal'tsev, L. A. // Ukrainian Mathematical Journal;Apr2003, Vol. 55 Issue 4, p588 

    We consider some harmonic mappings related to hyperbolic Gauss mappings and Gauss mappings in the Obata sense.

  • Some uniqueness theorems with truncated multiplicities of meromorphic mappings. Yan, Qiming // Chinese Annals of Mathematics;Oct2008, Vol. 29 Issue 5, p531 

    In this article, some uniqueness theorems of meromorphic mappings in several complex variables sharing hyperplanes in general position are proved with truncated multiplicities.

  • Maps with dense orbits: Ansari's theorem revisited and the infinite torus. Marano, Miguel; Salas, H�ctor N. // Bulletin of the Belgian Mathematical Society - Simon Stevin;Aug2009, Vol. 16 Issue 3, p481 

    Let B be a Banach space and T a bounded linear operator on B. A celebrated theorem of Ansari says that whenever T is hypercyclic so is any power Tn. We provide a very natural proof of this theorem by building on an approach by Bourdon. We also explore an extension to a non linear setting of a...

  • Polynomial Approximation of Functions on a Quasi-Smooth Arc with Hermitian Interpolation. Andrievskii, Vladimir; Blatt, Hans-Peter // Constructive Approximation;Aug2009, Vol. 30 Issue 1, p121 

    We construct polynomial approximations for continuous functions f defined on a quasi-smooth (in the sense of Lavrentiev) arc L in the complex plane which simultaneously interpolate f and its derivatives at given points of L.

  • Iterative Method for Set-Valued Mixed Quasivariational Inequalities in a Banach Space. Schaible, S.; Yao, J. C.; Zeng, L. C. // Journal of Optimization Theory & Applications;Jun2006, Vol. 129 Issue 3, p425 

    This paper introduces an iterative method for finding approximate solutions of a set-valued mixed quasivariational inequality in the setting of a Banach space. Existence of a solution of this rather general problem and the convergence of the proposed iterative method to a solution are established.

  • Equidistribution and Nevanlinna theory. David Drasin; Yûsuke Okuyama // Bulletin of the London Mathematical Society;Aug2007, Vol. 39 Issue 4, p603 

    Russakovskii and Shiffman quantified the equidistribution theorem of Brolin, Lyubich and Freire–Lopes–Mañé by showing that the (normalized) measures determined by counting preimages of a point a ∈ [double-struck C] converge exponentially to the equilibrium measure...

  • Explicit Quasiconformal Extensions of Planar Harmonic Mappings. Ganczar, Andrzej // Journal of Computational Analysis & Applications;Jan2008, Vol. 10 Issue 1, p179 

    Harmonic mappings appear in connection with the theory of minimal surfaces - a nonparametric minimal surface expressed in terms of isothermal parameters and projected onto its base plane induces a harmonic mapping. Intensive studies of these mappings were initiated by J. Clunie and T....

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics