An alternative approach to the
Faber-Krahn inequality for Robin problems

Dorin Bucur and Daniel Daners
Calculus of Variations and PDE's, 37(2010), 75 - 86
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)

A preprint (PDF) is available.

You can go to the original article.