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

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 th...

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Veröffentlicht in:	Calculus of variations and partial differential equations 2010-01, Vol.37 (1-2), p.75-86
Hauptverfasser:	Bucur, Dorin, Daners, Daniel
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Analysis of PDEs Boundary conditions Calculus of variations Calculus of Variations and Optimal Control Optimization Control Eigenvalues Inequalities Laplace transforms Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators Partial differential equations Proving Sharpness Systems Theory Theoretical
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Zusammenfassung:	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.
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-009-0252-3