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Extra info for The strong maximum principle revisited
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1). 2) reduces just to the manifold Laplacian, see , page 232. A specific example is given by the variational integral 1 √ |∇u|pg + F (u) dM, p > 1, where dM = gdx on Ω, Ω p √ introduced by Mossino (, page 40), though without the volume factor g. Here of course A(ρ) = ρp−2 , p > 1. Other examples are given also in . 13) when aij (x, u) = g(x)g ij (x), B(x, u, ξ) = g(x)f (u). 13). As at the beginning of the section, we assume that (A1) and (A2) are valid, and additionally that the tensors [g ij ] = [g ij (x, u)] and [aij ] = [aij (x, u)] are continuously differentiable, 36 P.
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