A simple proof of the optimal power in Liouville theorems

DOI10.5565/PUBLMAT6622212WikidataQ113689592 ScholiaQ113689592MaRDI QIDQ2154824

Salvador Villegas

Publication date: 15 July 2022

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.04400

zbMATH Keywords

Allen-Cahn equationLiouville theoremsDirichlet and potential energies

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Semilinear elliptic equations (35J61) Entire solutions to PDEs (35B08) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

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• On De Giorgi's conjecture in dimension \(N\geq 9\)
• On a conjecture of De Giorgi and some related problems
• Regularity of flat level sets in phase transitions
• Sharp Liouville theorems
• Sharp counterexamples related to the De Giorgi conjecture in dimensions $4\leq n \leq 8$
• A gradient bound and a liouville theorem for nonlinear poisson equations
• On the Liouville Property for Divergence Form Operators
• 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 a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

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