Faber-Krahn inequality for Robin problems

Calculus of Variations and PDE's, **37**(2010), 75 - 86

Original article at doi:10.1007/s00526-009-0252-3

Citations on Google Scholar

Original article at doi:10.1007/s00526-009-0252-3

Citations on Google Scholar

We give a simple proof of the Faber-Krahn inequality for the first
eigenvalue of the *p*-Laplace operator with Robin boundary conditions.
The techniques introduced allow to work with much less regular domains
by using test function arguments. We substantially simplify earlier
proofs, and prove the sharpness of the inequality for a larger class
of domains at the same time.

**AMS Subject Classification (2000):**
35P15, (35J25, 35J60)

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