Vol. 103, No. 2, 1982

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The two-obstacle problem for the biharmonic operator

Luis A. Caffarelli, Avner Friedman and Alessandro Torelli

Vol. 103 (1982), No. 2, 325–335
Abstract

In this work we consider a two-obstacle problem for the plate, namely, the problem of finding a minimizer u of

∫
|Δv |2dx, subject to (v− h) ∈ H2 (Ω), ϕ ≦ v ≦ ψ
Ω                            0

where Ω is a bounded domain in Rn; n = 2,3. We prove that u C1,1 and that, in general, uC2.

Mathematical Subject Classification 2000
Primary: 35J85
Secondary: 49A29
Milestones
Received: 29 September 1980
Published: 1 December 1982
Authors
Luis A. Caffarelli
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin TX 78712-0257
United States
http://www.ma.utexas.edu/users/caffarel/
Avner Friedman
Alessandro Torelli