𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On a conjecture for an overdetermined problem for the biharmonic operator

✍ Scribed by V. Goyal; P.W. Schaefer

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
146 KB
Volume
21
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

It has been proven that if the solution exists to an inhomogeneous biharmonic equation in the plane where the values of the solution, the normal derivative of the solution, and the Laplacian of the solution are prescribed on the boundary, then the domain is a disk. This result has been extended to N -dimensions by the Serrin reflection method. Here we present a new proof and give a characterization of open balls in R n .

πŸ“œ SIMILAR VOLUMES

Polygonal interface problems for the bih
Polygonal interface problems for the biharmonic operator
✍ Serge Nicaise πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 971 KB

## Abstract We study some boundary value problems on two‐dimensional polygonal topological networks, where on each face, the considered operator is the biharmonic operator. The transmission conditions we impose along the edges are inspired by the models introduced by H. Le Dret [13] and Destuynder

Asymptotic First Eigenvalue Estimates fo
Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle
✍ M.P. Owen πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 380 KB

We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is found by algebraic manipulation of the operator, and the upper b