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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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DOI

10.1016/j.acn.2004.01.001

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1432-0835

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On Newton equations which are totally integrable a

Authors: Misha Bialy
Publish Date: 2016/05/12
Volume: 55, Issue: 3, Pages: 51-
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Abstract

In this paper Hamiltonian system of time dependent periodic Newton equations is studied It is shown that for dimensions 3 and higher the following rigidity results holds true if all the orbits in a neighborhood of infinity are action minimizing then the potential must be constant This gives a generalization of the previous result Bialy and Polterovich Math Res Lett 26695–700 1995 where it was required all the orbits to be minimal As a result we have the following application suppose that for the time1 map of the Hamiltonian flow there exists a neighborhood of infinity which is filled by invariant Lagrangian tori homologous to the zero section Then the potential must be constant Remarkably the statement is false for n=1 case and remains unknown to the author for n=2

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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. Energy asymptotics for Type II superconductors
  15. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
  16. Singular points of Hölder asymptotically optimally doubling measures
  17. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
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  20. Boundary value problems for Willmore curves in $$\mathbb {R}^2$$
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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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