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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 54
  3. Calculus of Variations and Partial Differential Equations : Volume 54, Issue 3, November 2015
  4. Critical O(d)-equivariant biharmonic maps
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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 54, Issue 4, December 2015
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 3, November 2015
Nonlocal quantitative isoperimetric inequalities
Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities
Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the torus
Regularity of $$C^1$$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds
Transition fronts for periodic bistable reaction-diffusion equations
Multiple brake orbits in $$m$$ -dimensional disks
Stress regularity for a new quasistatic evolution model of perfectly plastic plates
Dirac-geodesics and their heat flows
Representation of Markov chains by random maps: existence and regularity conditions
Higher dimensional solitary waves generated by second-harmonic generation in quadratic media
Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
Sequential weak approximation for maps of finite Hessian energy
Reinforcement problems for variational inequalities on fractal sets
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in $${\mathbb {R}}^N$$
I-properness of Mabuchi’s K-energy
Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
On the topology of translating solitons of the mean curvature flow
Two closed geodesics on $${\mathbb {R}}P^{2n+1}$$ with a bumpy Finsler metric
Critical O(d)-equivariant biharmonic maps
Some rigidity results on critical metrics for quadratic functionals
Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations
Ground state solutions of scalar field fractional Schrödinger equations
Construction of blow-up sequences for the prescribed scalar curvature equation on $$S^n$$ . III. Aggregated and towering blow-ups
Sobolev regularity for the first order Hamilton–Jacobi equation
Standing waves for a class of Kirchhoff type problems in $${\mathbb {R}^3}$$ involving critical Sobolev exponents
Global Lorentz and Lorentz–Morrey estimates below the natural exponent for quasilinear equations
Rate of decay for the mass ratio of pseudo-holomorphic integral 2-cycles
Finite Morse index solutions of weighted elliptic equations and the critical exponents
Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms
Quantitative isoperimetric inequalities in $$\mathbb {H}^n$$
Geometric stability of the Coulomb energy
Global smooth axisymmetric solutions of 3-D inhomogeneous incompressible Navier–Stokes system
On positive solutions for (p, q)-Laplace equations with two parameters
Fractional porous media equations: existence and uniqueness of weak solutions with measure data
On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space III
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 2, October 2015
Calculus of Variations and Partial Differential Equations : Volume 54, Issue 1, September 2015
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 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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Critical O(d)-equivariant biharmonic maps

Content Provider SpringerLink
Author Cooper, Matthew K.
Copyright Year 2015
Abstract We study O(d)-equivariant biharmonic maps in the critical dimension. A major consequence of our study concerns the corresponding heat flow. More precisely, we prove that blowup occurs in the biharmonic map heat flow from $$B^4(0, 1)$$ into $$S^4$$ . To our knowledge, this was the first example of blowup for the biharmonic map heat flow. Such results have been hard to prove, due to the inapplicability of the maximum principle in the biharmonic case. Furthermore, we classify the possible O(4)-equivariant biharmonic maps from $$\mathbf {R}^4$$ into $$S^4$$ , and we show that there exists, in contrast to the harmonic map analogue, equivariant biharmonic maps from $$B^4(0,1)$$ into $$S^4$$ that wind around $$S^4$$ as many times as we wish. We believe that the ideas developed herein could be useful in the study of other higher-order parabolic equations.
Ending Page 2919
Page Count 25
Starting Page 2895
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3
Volume Number 54
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2015-07-28
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Initial-boundary value problems for higher-order parabolic equations Boundary value problems for higher-order elliptic equations Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Harmonic maps etc. Nonlinear boundary value problems for linear elliptic equations Nonlinear elliptic equations Nonlinear parabolic equations Asymptotic behavior of solutions Growth, boundedness
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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