Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions

Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions

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by Hans-christoph Grunau , Guido Sweers

BibTeX

@MISC{Grunau_optimalsobolev,
    author = {Hans-christoph Grunau and Guido Sweers},
    title = {Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions},
    year = {}
}

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Abstract

We prove that the best constant for the critical embedding of higher order Sobolev spaces does not depend on all the traces. The proof uses a comparison principle due to Talenti [19] and an extension argument which enables us to extend radial functions from the ball to the whole space with no increase of the Dirichlet norm. Similar arguments may also be used to prove the very same result for Hardy-Rellich inequalities. AMS Classification: primary 46E35, secondary 26D10, 35J55 Keywords: optimal constant, Sobolev embedding, Hardy-Rellich inequality

Citations

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