Abstract
In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given measure. Instead of treating this variational problem with a volume constraint, we introduce a problem without any constraints, but with a penalty term. We concentrate on the minimizing function and prove that it has Lipschitz continuous first derivatives. Furthermore, we show that the penalized problem and the original problem can be treated as equivalent. Finally, we establish some qualitative properties of the free boundary.
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Acknowledgments
This work is part of the author’s Ph.D. Thesis at the RWTH Aachen University. The author is very grateful to her advisor Alfred Wagner for many helpful discussions and his continuous support. The author also likes to thank the referee for pointing out an error in an earlier version of this work.
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Communicated by L. Ambrosio.
