Convexity of the first eigenfunction of the drifting Laplacian operator and its applications.

Ma, Li; Liu, Baiyu

Displaying similar documents to “Convexity of the first eigenfunction of the drifting Laplacian operator and its applications.”

Estimates of the first eigenvalue of a big cup domain of a 2-sphere

Tadayuki Matsuzawa, Shukichi Tanno (1982)

Compositio Mathematica

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Superharmonicity of nonlinear ground states.

Peter Lindqvist, Juan Manfredi, Eero Saksman (2000)

Revista Matemática Iberoamericana

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The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operator Δ_pu = div (|∇u|^p-2 ∇u) is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δ_p is the positive solution with boundary values zero of the equation div(|∇u|^p-2 ∇u) + λ |u|^p-2 u = 0 in the bounded domain...

Liouville type theorems for φ-subharmonic functions.

Marco Rigoli, Alberto G. Setti (2001)

Revista Matemática Iberoamericana

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In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.