scientific article; zbMATH DE number 1898308

zbMath1014.35019MaRDI QIDQ4802648

Isabeau Birindelli, Jyotshana V. Prajapat

Publication date: 22 April 2003

Full work available at URL: http://www.numdam.org/item?id=ASNSP_2001_4_30_2_269_0

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zbMATH Keywords

semilinear elliptic equationsHeisenberg LaplacianDe Giorgi conjectureone dimensional symmetry

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Hypoelliptic equations (35H10)

Related Items (7)

Maximum principle on unbounded domains for sub-Laplacians: A potential theory approach ⋮ A Liouville-type theorem for fully nonlinear CR invariant equations on the Heisenberg group ⋮ Large sets at infinity and maximum principle on unbounded domains for a class of sub-elliptic operators ⋮ Maximum principles and monotonicity of solutions for fractional \(p\)-equations in unbounded domains ⋮ On fully nonlinear CR invariant equations on the Heisenberg group ⋮ Stable solutions of symmetric systems involving hypoelliptic operators ⋮ An application of a global lifting method for homogeneous Hörmander vector fields to the Gibbons conjecture

Cites Work

• Monotonicity and symmetry results for degenerate elliptic equations on nilpotent Lie groups.
• On a conjecture of De Giorgi and some related problems
• Superharmonic functions in the Heisenberg group: estimates and Liouville theorems
• One-dimensional symmetry of bounded entire solutions of some elliptic equations
• Symmetry for solutions of semilinear elliptic equations in \(\mathbb{R}^N\) and related conjectures
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Hopf's lemma and anti-maximum principle in general domains
• Boundary regularity in the dirichlet problem for □b on cr manifolds
• Nonlinear liouville theorems in the heisenberg group vip the moving plane method
• 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
• Non‐coercive boundary value problems
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