Solutions of the Allen-Cahn equation which are invariant under screw-motion
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Publication:431146
DOI10.1007/s00229-011-0492-3zbMath1246.35093OpenAlexW2045937921MaRDI QIDQ431146
Monica Musso, Frank Pacard, Manuel A. del Pino
Publication date: 26 June 2012
Published in: Manuscripta Mathematica (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/10533/127587
Variational methods involving nonlinear operators (47J30) Variational methods for second-order elliptic equations (35J20) Entire solutions to PDEs (35B08) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)
Related Items (12)
Spiraling solutions of nonlinear Schrödinger equations ⋮ Solutions to the Allen Cahn equation and minimal surfaces ⋮ Rotationally symmetric solutions to the Cahn-Hilliard equation ⋮ Periodic solutions to a Cahn-Hilliard-Willmore equation in the plane ⋮ Generalizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean space ⋮ On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains ⋮ Traveling vortex helices for Schrödinger map equations ⋮ Helicoids and catenoids in \(M\times \mathbb{R} \) ⋮ Solutions of the fractional Allen–Cahn equation which are invariant under screw motion ⋮ Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice ⋮ Interacting helical vortex filaments in the three-dimensional Ginzburg-Landau equation ⋮ The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit
Cites Work
- Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in \(\mathbb{R}^3\)
- On De Giorgi's conjecture in dimension \(N\geq 9\)
- Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
- Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
- The monotonicity of the period function for planar Hamiltonian vector fields
- Saddle solutions of the bistable diffusion equation
- Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations
- BIFURCATION FROM SIMPLE EIGENVALUES AND EIGENVALUES OF GEOMETRIC MULTIPLICITY ONE
- Moduli space theory for the Allen-Cahn equation in the plane
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