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When are superharmonic functions concave? Applications to the St. Venant torsion problem and to the fundamental mode of the clamped membrane. (English) Zbl 0581.73006
The author examines properties of superharmonic functions. He discusses the implications in the St. Venant torsion problem, in the clamped membrane, and in problems involving starshapedness. A number of theorems and proofs are presented.
The paper is carefully written. It is concise. It should be of interest to both elasticians and mathematicians.
Reviewer: R.L.Huston

MSC:
74G50 Saint-Venant’s principle
52A10 Convex sets in \(2\) dimensions (including convex curves)
74K15 Membranes
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References:
[1] Fan, Amer. Math. Monthly 60 pp 48– (1953)
[2] ; , Inequalities, Berlin-Göttingen-Heidelberg 1961.
[3] Heinrich, ZAMM 63 pp 65– (1983)
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