A relation of the Allen-Cahn equations and the Euler equations and applications of the equipartition

DOI10.1007/s00030-023-00888-2zbMath1525.35088arXiv2203.13960OpenAlexW4387399284MaRDI QIDQ6072388

Dimitrios Gazoulis

Publication date: 13 October 2023

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13960

zbMATH Keywords

Euler equationsAllen-Cahn systemAllen-Cahn equationsequipartition of the energy

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Semilinear elliptic equations (35J61) Second-order elliptic systems (35J47)

Related Items (1)

On the triple junction problem without symmetry hypotheses

Cites Work

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• On De Giorgi's conjecture in dimension \(N\geq 9\)
• Uniqueness and stability of saddle-shaped solutions to the Allen-Cahn equation
• Symmetry and related properties via the maximum principle
• 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
• Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions.
• Finite energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in \(\mathbb R^K\).
• Elliptic systems of phase transition type
• Regularity of flat level sets in phase transitions
• Minimal cones and the Bernstein problem
• A Bernstein-type theorem for minimal graphs over convex domains
• Vorticity and Incompressible Flow
• Distance Functions and Almost Global Solutions of Eikonal Equations
• Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
• A gradient bound and a liouville theorem for nonlinear poisson equations
• A gradient bound for entire solutions of quasi‐linear equations and its consequences
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
• On Almost Entire Solutions Of The Burgers Equation
• Gradient estimates for semilinear elliptic systems and other related results

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