Glasnik Matematicki, Vol. 34, No.1 (1999), 5-10.

LIFTING A CIRCULAR MEMBRANE BY UNITARY FORCES

Lucio R. Berrone

Abstract.   Let Ω be a convex membrane. We lift certain parts Γ of its boundary by means of unitary forces while the remaining parts are maintained at level 0. Call u[Γ] the position that the such lifted membrane assumes. When the parts Γ are varying on ∂Ω so that their total lenght C is preserved, it has been conjectured that the functional Γ ||u(Γ)||_p attain its maximum value for a certain conected arc of lenght C. In this paper we present a proof of this conjecture for the case in which Ω is a circle and p = 1.

1991 Mathematics Subject Classification.   31A05, 31A15.