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Regularizing effects of homogeneous evolution equations: the case of homogeneity order zero

  • Daniel HauerEmail author
  • José M. Mazón
Article
  • 17 Downloads

Abstract

In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous operators of order zero are strong solutions; in particular, the first-order time derivative satisfies a global regularity estimate depending only on the initial value and the positive time. We apply those results to the Cauchy problem associated with the total variational flow operator and the nonlocal fractional 1-Laplace operator.

Keywords

Nonlinear semigroups Local and nonlocal operators 1-Laplace operator Regularity Homogenous operators 

Mathematics Subject Classification

47H20 47H06 47J35 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of SydneySydneyAustralia
  2. 2.Departament d’Anàlisi MatemàticaUniversitat de ValènciaValenciaSpain

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