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 Δpu = 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 equation div(|∇u|p-2 ∇u) + λ |u|p-2 u = 0 in the bounded domain...