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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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1432-0835

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Boundary value problems for Willmore curves in

Authors: Rainer Mandel
Publish Date: 2015/10/24
Volume: 54, Issue: 4, Pages: 3905-3925
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Abstract

Let A=00B=10 and theta 1=theta 2in 0pi /2 Then the Dirichlet problem 1 has infinitely many axially symmetric solutions gamma 1j and infinitely many axially nonsymmetric solutions gamma 2j satisfying Wgamma 1jWgamma 2jrightarrow infty as jrightarrow infty The existence of infinitely many axially symmetric solutions gamma 1j jin mathbb N 0 of 1 follows from Theorem 4 Corollary 1 and the fact that for every eta in 1+1 and every jin mathbb N 0 a solution of 32 is given by sigma 1=1sigma 2=1z=barz=eta cos theta 11/2 The formula for a and W from Theorem 4 implies that these solutions satisfy Wgamma 1jrightarrow infty as jrightarrow infty and sigma 1mathrmcn1z+sigma 2mathrmcn1barz=0 implies that gamma 1j is axially symmetric

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  1. Asymptotic behavior at isolated singularities for solutions of nonlocal semilinear elliptic systems of inequalities
  2. Fractional Poincaré inequality with finite total Q -curvature
  3. Solitary waves for a class of quasilinear Schrödinger equations in dimension two
  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
  5. On elliptic systems with Sobolev critical growth
  6. Critical points for functionals with quasilinear singular Euler–Lagrange equations
  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
  9. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
  10. Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
  11. Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
  12. Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
  13. Sharp energy estimates for nonlinear fractional diffusion equations
  14. On Newton equations which are totally integrable at infinity
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  16. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
  17. Singular points of Hölder asymptotically optimally doubling measures
  18. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
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  20. A mean field type flow part I: compactness of solutions to a perturbed mean field type equation
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  22. On a quasilinear system involving the operator curl
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  24. Moser–Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2
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