for Robin problems in any space dimension

Preprint (PDF)
21 October 2005

Mathematische Annalen**335** (2006), 767 - 785.

Original article at doi:10.1007/s00208-006-0753-8

Citations on Google Scholar

Mathematische Annalen

Original article at doi:10.1007/s00208-006-0753-8

Citations on Google Scholar

We prove a Faber-Krahn inequality for the first eigenvalue of
the Laplacian with Robin boundary conditions, asserting that
amongst all Lipschitz domains of fixed volume, the ball has the
smallest first eigenvalue. We prove the result in all space
dimensions using ideas from [M.-H. Bossel, C. R. Acad.
Sci. Paris Sér. I Math. **302** (1986), 47-50], where
a proof for smooth domains in the plane was given. The method
avoids the use of symmetrisation arguments. The results also imply
variants of the Cheeger inequality for the first eigenvalue.

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