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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 45
  3. Calculus of Variations and Partial Differential Equations : Volume 45, Issue 3-4, November 2012
  4. $${\mathcal{F}}$$ -stability of self-similar solutions to harmonic map heat flow
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 45, Issue 3-4, November 2012
Regularity of the nodal set of segregated critical configurations under a weak reflection law
Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties
$${\mathcal{F}}$$ -stability of self-similar solutions to harmonic map heat flow
Sharp bounds on the volume fractions of two materials in a two-dimensional body from electrical boundary measurements: the translation method
Nonlinear gradient estimates for elliptic equations of general type
An optimal Hardy–Morrey inequality
Existence and multiplicity results for Pucci’s operators involving nonlinearities with zeros
Isoperimetric inequalities for minimal submanifolds in Riemannian manifolds: a counterexample in higher codimension
A new bound on the Morse index of constant mean curvature tori of revolution in $${{\mathbb{S}}^{3}}$$
Perelman’s lambda-functional and the stability of Ricci-flat metrics
The Cauchy problem for wave maps on a curved background
Calculus of Variations and Partial Differential Equations : Volume 45, Issue 1-2, September 2012
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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$${\mathcal{F}}$$ -stability of self-similar solutions to harmonic map heat flow

Content Provider SpringerLink
Author Zhang, Yongbing
Copyright Year 2011
Abstract Inspired by the work of Colding and Minicozzi II: ”Generic mean curvature flow I: generic singularities”, we explore the notion of generic singularities for the harmonic map heat flow. We introduce $${\mathcal{F}}$$ -functional and entropy for maps from Euclidean spaces. The critical points of the $${\mathcal{F}}$$ -functional are exactly the weakly self-similar solutions to the harmonic map heat flow. We define the notion of $${\mathcal{F}}$$ -stability for weakly self-similar solutions. The $${\mathcal{F}}$$ -stability can be characterized by the semi-positive definiteness of the Jacobi operator acting on a subspace of variation fields.
Ending Page 366
Page Count 20
Starting Page 347
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 45
Language English
Publisher Springer-Verlag
Publisher Date 2011-10-27
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Differential geometric aspects of harmonic maps Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Theoretical, Mathematical and Computational Physics Analysis
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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