1. A Resolution of the Poisson Problem for Elastic Plates.
- Author
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Da Lio, Francesca, Palmurella, Francesco, and Rivière, Tristan
- Subjects
- *
ELASTIC plates & shells , *NUMERICAL solutions to Poisson's equation - Abstract
We consider the problem of finding a surface Σ ⊂ R m of least Willmore energy among all immersed surfaces having the same boundary, boundary Gauss map and area. Such a problem was considered by S. Germain and S.D. Poisson in the early XIX century as a model for equilibria of thin, clamped elastic plates. We present a solution in the case of boundary data of class C 1 , 1 and for when the boundary curve is simple and closed. The minimum is realised by an immersed disk, possibly with a finite number of branch points in its interior, which is of class C 1 , α up to the boundary for some 0 < α < 1 , and whose Gauss map extends to a map of class C 0 , α up to the boundary. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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