A Sobolev non embedding

  • Petru Mironescu

    Université Lyon 1, Villeurbanne, France
  • Winfried Sickel

    Friedrich-Schiller-Universität Jena, Germany

Abstract

If Ω\Omega is a bounded domain in Rn\mathbb R^n, 1q<p1 ≤ q < p ≤ \infty and s=0,1,2,s=0, 1, 2,\ldots, then we clearly have Ws,p(Ω)Ws,q(Ω)W^{s,p}(\Omega)\subset W^{s,q}(\Omega). We prove that this property does not hold when ss in not an integer.

Cite this article

Petru Mironescu, Winfried Sickel, A Sobolev non embedding. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 3, pp. 291–298

DOI 10.4171/RLM/707