JournalsaihpcVol. 36, No. 3pp. 861–885

Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains

  • Simon Zugmeyer

    Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains cover

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Abstract

We find a new sharp trace Gagliardo–Nirenberg–Sobolev inequality on convex cones, as well as a sharp weighted trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell–Brascamp–Lieb inequality, coming from the Brunn–Minkowski theory.

Cite this article

Simon Zugmeyer, Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 3, pp. 861–885

DOI 10.1016/J.ANIHPC.2018.11.001