Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)

Lineia Schutz; Juliana S. Ziebel; Janaina P. Zingano; Paulo R. Zingano

Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)

Functional Analysis 2016-02-08 v1

Authors: Lineia Schutz , Juliana S. Ziebel , Janaina P. Zingano , Paulo R. Zingano

Abstract

We obtain the optimal value of the constant K(n,s) in the Sobolev-Nirenberg-Gagliardo inequality $\|\,u\,\|_{L^{\infty}(\mathbb{R}^{n})} \leq K(n,s) \,\|\, u \,\|_{L^{2}(\mathbb{R}^{n})}^{1 - n/(2s)} \|\, u \,\|_{\dot{H}^{s}(\mathbb{R}^{n})}^{n/(2s)}$ where $s > n/2$ .

Keywords

sobolev inequalities sobolev regularity of partial differential equations function spaces and inequalities

Cite

@article{arxiv.1602.01902,
  title  = {Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)},
  author = {Lineia Schutz and Juliana S. Ziebel and Janaina P. Zingano and Paulo R. Zingano},
  journal= {arXiv preprint arXiv:1602.01902},
  year   = {2016}
}

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5 pages

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