Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions
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Publication:424422
DOI10.1016/j.jde.2012.03.004zbMath1250.35078arXiv1102.4022OpenAlexW1989418172MaRDI QIDQ424422
Publication date: 1 June 2012
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1102.4022
monotonicityMorse indexlevel setAllen-Cahn equationsaddle solutionseven symmetryHamiltonian identity
Minimal surfaces and optimization (49Q05) Nonlinear elliptic equations (35J60) Curves in Euclidean and related spaces (53A04) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)
Related Items (18)
A Harnack inequality for the parabolic Allen-Cahn equation ⋮ On De Giorgi's conjecture: recent progress and open problems ⋮ Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane ⋮ On variational characterization of four-end solutions of the Allen-Cahn equation in the plane ⋮ Saddle solutions for bistable symmetric semilinear elliptic equations ⋮ Two-end solutions to the Allen-Cahn equation in \(\mathbb{R}^3\) ⋮ Four end solutions of a free boundary problem ⋮ Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in \({\mathbb R}^2\) ⋮ Double-well phase transitions are more rigid than minimal hypersurfaces ⋮ Existence of heteroclinic and saddle-type solutions for a class of quasilinear problems in whole ℝ2 ⋮ The p-widths of a surface ⋮ Allen-Cahn min-max on surfaces ⋮ End-to-end construction for the Allen-Cahn equation in the plane ⋮ Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\) ⋮ Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a super-spherical sector ⋮ Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\) ⋮ Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a sub-spherical sector ⋮ Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice
Cites Work
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- On De Giorgi's conjecture in dimension \(N\geq 9\)
- The space of 4-ended solutions to the Allen-Cahn equation in the plane
- On stable critical points for a singular perturbation problem
- Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
- Saddle-type solutions for a class of semilinear elliptic equations
- Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
- On complete minimal surfaces with finite Morse index in three manifolds
- Saddle solutions of the bistable diffusion equation
- On a conjecture of De Giorgi and some related problems
- Stationary layered solutions in \(\mathbb{R}^ 2\) for an Allen-Cahn system with multiple well potential
- On De Giorgi's conjecture in dimensions 4 and 5
- Symmetry of traveling wave solutions to the Allen-Cahn equation in \({\mathbb R^{2}}\)
- Regularity of flat level sets in phase transitions
- The classification of four-end solutions to the Allen-Cahn equation on the plane
- Hamiltonian identities for elliptic partial differential equations
- Qualitative Properties of Saddle-Shaped Solutions to Bistable Diffusion Equations
- Axial symmetry of some steady state solutions to nonlinear Schrödinger equations
- Nondegeneracy of the saddle solution of the Allen-Cahn equation
- The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends
- Symmetry of global solutions to a class of fully nonlinear elliptic equations in 2D
- A gradient bound and a liouville theorem for nonlinear poisson equations
- The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- CONVERGENCE TO EQUILIBRIUM FOR SEMILINEAR PARABOLIC PROBLEMS IN
- On the stability of the saddle solution of Allen–Cahn's equation
- Moduli space theory for the Allen-Cahn equation in the plane
- Ginzburg-Landau vortices
- Qualitative properties of some bounded positive solutions to scalar field equations
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