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

Dorin Bucur (1) , Daniel Daners

1 LAMA - Laboratoire de Mathématiques

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 establish the sharpness of the inequality for a larger class of domains at the same time.

Domaines: Equations aux dérivées partielles [math.AP]

Dorin Bucur, Daniel Daners. An alternative approach to the Faber-Krahn inequality for Robin problems. Calculus of Variations and Partial Differential Equations, 2010, 37 (1-2), pp.75-86. ⟨10.1007/s00526-009-0252-3⟩. ⟨hal-00387028⟩