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A quantitative stability estimate for the fractional Faber-Krahn inequality (1901.10845v2)
Published 30 Jan 2019 in math.AP and math.OC
Abstract: We prove a quantitative version of the Faber-Krahn inequality for the first eigenvalue of the fractional Dirichlet-Laplacian of order s. This is done by using the so-called Caffarelli-Silvestre extension and adapting to the nonlocal setting a trick by Hansen and Nadirashvili. The relevant stability estimate comes with an explicit constant, which is stable as the fractional order of differentiability goes to 1.