Sharp counterexamples related to the De Giorgi conjecture in dimensions $4\leq n \leq 8$

DOI10.1090/S0002-9939-2013-12040-XzbMath1282.35110OpenAlexW1545283201WikidataQ122899822 ScholiaQ122899822MaRDI QIDQ2862183

Amir Moradifam

Publication date: 14 November 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-12040-x

zbMATH Keywords

Liouville comparison principle

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Entire solutions to PDEs (35B08) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (2)

A simple proof of the optimal power in Liouville theorems ⋮ Sharp Liouville theorems

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
• New Liouville theorems for linear second order degenerate elliptic equations in divergence form.
• Regularity of flat level sets in phase transitions
• On the Liouville Property for Divergence Form Operators
• Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi

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