Hypercontractivity, Gagliardo–nirenberg Inequalities and Subordination for Classes of Nonlinear Semigroups

  • FABIO CIPRIANI
  • Published 2008

Abstract

A suitable notion of hypercontractivity for a nonlinear semigroup {Tt} is shown to imply Gagliardo–Nirenberg inequalities for its generator H , provided a subhomogeneity property holds for the energy functional (u, Hu). We use this fact to prove that, for semigroups generated by operators of p–Laplacian–type, hypercontractivity implies ultracontractivity… (More)

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