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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 48
  3. Calculus of Variations and Partial Differential Equations : Volume 48, Issue 3-4, November 2013
  4. Unstable Willmore surfaces of revolution subject to natural boundary conditions
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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 48, Issue 3-4, November 2013
An extremal case of the equation of prescribed Weingarten curvature
Unstable Willmore surfaces of revolution subject to natural boundary conditions
Derivation of a rod theory for biphase materials with dislocations at the interface
Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case
Local behaviour of singular solutions for nonlinear elliptic equations in divergence form
Geodesics for a class of distances in the space of probability measures
Fractional harmonic maps into manifolds in odd dimension n > 1
On the isoperimetric problem for radial log-convex densities
Global existence for the Cauchy problem of the parabolic–parabolic Keller–Segel system on the plane
Conformal invariants measuring the best constants for Gagliardo–Nirenberg–Sobolev inequalities
A spinorial characterization of hyperspheres
Nonuniqueness of infinity ground states
Sharp constants in weighted trace inequalities on Riemannian manifolds
Infinitely many solutions for an elliptic problem involving critical Sobolev and Hardy–Sobolev exponents
Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents
On functions whose symmetric part of gradient agree and a generalization of Reshetnyak’s compactness theorem
On the Aleksandrov–Bakelman–Pucci estimate for the infinity Laplacian
An optimal constant for the existence of least energy solutions of a coupled Schrödinger system
Exact multiplicity results for a singularly perturbed Neumann problem
Calculus of Variations and Partial Differential Equations : Volume 48, Issue 1-2, September 2013
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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Unstable Willmore surfaces of revolution subject to natural boundary conditions

Content Provider SpringerLink
Author Deckelnick, Klaus Wheeler, Glen Dall’Acqua, Anna
Copyright Year 2012
Abstract In the class of surfaces with fixed boundary, critical points of the Willmore functional are naturally found to be those solutions of the Euler-Lagrange equation where the mean curvature on the boundary vanishes. We consider the case of symmetric surfaces of revolution in the setting where there are two families of stable solutions given by the catenoids. In this paper we demonstrate the existence of a third family of solutions which are unstable critical points of the Willmore functional, and which spatially lie between the upper and lower families of catenoids. Our method does not require any kind of smallness assumption, and allows us to derive some additional interesting qualitative properties of the solutions.
Ending Page 313
Page Count 21
Starting Page 293
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 48
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2012-08-28
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Methods involving semicontinuity and convergence; relaxation Boundary value problems for higher-order elliptic equations Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Critical points Analysis Theoretical, Mathematical and Computational Physics Optimization of shapes other than minimal surfaces
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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