Abstract
In general, higher order elliptic equations and boundary value problems like the biharmonic equation or the linear clamped plate boundary value problem do not enjoy neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property. It is shown that, on the other hand, for bounded smooth domains Ω ⊂ R n , the negative part of the corresponding Green's function is “small” when compared with its singular positive part, provided that n ⩾ 3 . To cite this article: H.-Ch. Grunau, F. Robert, C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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