Allen-Cahn equation for the truncated Laplacian: unusual phenomena

DOI10.3934/mine.2020034zbMath1489.35082arXiv2002.04565OpenAlexW3039951902MaRDI QIDQ2128550

Isabeau Birindelli, Giulio Galise

Publication date: 22 April 2022

Published in: Mathematics in Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.04565

zbMATH Keywords

fully nonlinear degenerate elliptic equationsAllen-Cahn type equationentire viscosity solutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Viscosity solutions to PDEs (35D40)

Cites Work

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• Propagating terraces in a proof of the Gibbons conjecture and related results
• On De Giorgi's conjecture in dimension \(N\geq 9\)
• Monotonicity and symmetry results for degenerate elliptic equations on nilpotent Lie groups.
• Towards a reversed Faber-Krahn inequality for the truncated Laplacian
• Multidimensional nonlinear diffusion arising in population genetics
• On a conjecture of De Giorgi and some related problems
• A negative answer to a one-dimensional symmetry problem in the Heisenberg group
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• A family of degenerate elliptic operators: maximum principle and its consequences
• The speed of propagation for KPP type problems. I: Periodic framework
• Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
• Liouville theorems for a family of very degenerate elliptic nonlinear operators
• Existence through convexity for the truncated Laplacians
• Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications
• Symmetry for solutions of two-phase semilinear elliptic equations on hyperbolic space
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• On the method of moving planes and the sliding method

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