Explicit optimal constants of two critical Rellich inequalities for radially symmetric functions

2020/02/12 by Sano, Megumi
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2002.04768

Abstract

We consider two critical Rellich inequalities with singularities at both the origin and the boundary in the higher order critical radial Sobolev spaces W_0, \rm rad^{k, p}, where 1< p = (N)/(k). We give the explicit values of the optimal constants of two critical Rellich inequalities for radially symmetric functions in W_0, \rm rad^{k, (N)/(k)}. Furthermore the (non-)attainability of the optimal constants are also discussed.

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