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Existence of an optimal domain for the buckling load of a clamped plate with prescribed volume

Published 14 Oct 2021 in math.AP and math.OC | (2110.07299v1)

Abstract: We formulate the minimization of the buckling load of a clamped plate as a free boundary value problem with a penalization term for the volume constraint. As the penalization parameter becomes small we show that the optimal shape problem with prescribed volume is solved. In addition, we discuss two different choices for the penalization term.

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