A proof of the Faber-Krahn inequality for the first eigenvalue of thep-Laplacian
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In this work we present an elementary proof of the Faber-Krahn inequality for the first eigenvalue of the p-Laplacian on bounded domains in ℝn. Let λ1 be the first eigenvalue and λ 1 * be the first eigenvalue for the ball of the same volume. Then we show that λ1=λ 1 * iff the domain is a ball. Our proof makes considerable use of the corresponding Talenti's inequality and some well known properties of the first eigenfunction.
KeywordsElliptic Equation Maximal Function Measure Zero Orlicz Space Isoperimetric Inequality
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