The space of 4-ended solutions to the Allen-Cahn equation in the plane
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Publication:713200
DOI10.1016/j.anihpc.2012.04.003zbMath1254.35219arXiv1106.1991OpenAlexW2008921158MaRDI QIDQ713200
Michał Kowalczyk, Yong Liu, Frank Pacard
Publication date: 26 October 2012
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.1991
Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08) PDEs in connection with statistical mechanics (35Q82)
Related Items (17)
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 \({\mathbb R}^2\) ⋮ Layered solutions with multiple asymptotes for non autonomous Allen-Cahn equations in \({\mathbb {R}^{3}}\) ⋮ The p-widths of a surface ⋮ Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions ⋮ On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg ⋮ Allen-Cahn min-max on surfaces ⋮ End-to-end construction for the Allen-Cahn equation in the plane ⋮ Phase-field approximations of the Willmore functional and flow ⋮ Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\) ⋮ Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice
Cites Work
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- Saddle solutions of the bistable diffusion equation
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- Regularity of flat level sets in phase transitions
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- Nondegeneracy of the saddle solution of the Allen-Cahn equation
- The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- On the stability of the saddle solution of Allen–Cahn's equation
- Moduli space theory for the Allen-Cahn equation in the plane
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