Best constant in Poincaré inequalities with traces: A free discontinuity approach

  • Dorin Bucur

    Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA 73000 Chambéry, France
  • Alessandro Giacomini

    DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Branze 43, 25123 Brescia, Italy
  • Paola Trebeschi

    DICATAM, Sezione di Matematica, Università degli Studi di Brescia, Via Branze 43, 25123 Brescia, Italy
Best constant in Poincaré inequalities with traces: A free discontinuity approach cover
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Abstract

For open bounded and with a Lipschitz boundary, and , we consider the Poincaré inequality with trace term

on the Sobolev space . We show that among all domains with prescribed volume, the constant is minimal on balls. The proof is based on the analysis of a free discontinuity problem.

Cite this article

Dorin Bucur, Alessandro Giacomini, Paola Trebeschi, Best constant in Poincaré inequalities with traces: A free discontinuity approach. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, pp. 1959–1986

DOI 10.1016/J.ANIHPC.2019.07.007