# Superharmonicity of nonlinear ground states.

Peter Lindqvist; Juan Manfredi; Eero Saksman

Revista Matemática Iberoamericana (2000)

- Volume: 16, Issue: 1, page 17-28
- ISSN: 0213-2230

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topLindqvist, Peter, Manfredi, Juan, and Saksman, Eero. "Superharmonicity of nonlinear ground states.." Revista Matemática Iberoamericana 16.1 (2000): 17-28. <http://eudml.org/doc/39587>.

@article{Lindqvist2000,

abstract = {The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operatorΔpu = div (|∇u|p-2 ∇u)is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equationdiv(|∇u|p-2 ∇u) + λ |u|p-2 u = 0in the bounded domain Ω in the n-dimensional Euclidean space.},

author = {Lindqvist, Peter, Manfredi, Juan, Saksman, Eero},

journal = {Revista Matemática Iberoamericana},

keywords = {Ecuación de Laplace; Función armónica; Ecuaciones en derivadas parciales no lineales; -Laplacian; eigenfunction; superharmonicity},

language = {eng},

number = {1},

pages = {17-28},

title = {Superharmonicity of nonlinear ground states.},

url = {http://eudml.org/doc/39587},

volume = {16},

year = {2000},

}

TY - JOUR

AU - Lindqvist, Peter

AU - Manfredi, Juan

AU - Saksman, Eero

TI - Superharmonicity of nonlinear ground states.

JO - Revista Matemática Iberoamericana

PY - 2000

VL - 16

IS - 1

SP - 17

EP - 28

AB - The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operatorΔpu = div (|∇u|p-2 ∇u)is a superharmonic function, provided that 2 ≤ p ≤ ∞. The ground state of Δp is the positive solution with boundary values zero of the equationdiv(|∇u|p-2 ∇u) + λ |u|p-2 u = 0in the bounded domain Ω in the n-dimensional Euclidean space.

LA - eng

KW - Ecuación de Laplace; Función armónica; Ecuaciones en derivadas parciales no lineales; -Laplacian; eigenfunction; superharmonicity

UR - http://eudml.org/doc/39587

ER -

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