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Harmonic and Trace Inequalities in Lipschitz Domains

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • Soumia Touhami

    (Faculté des Sciences, Laboratoire de Mathématiques et leures Applications, Equipe EDP et Calcul Scientifique, Moulay Ismail University)

  • Abdellatif Chaira

    (Faculté des Sciences, Laboratoire de Mathématiques et leures Applications, Equipe EDP et Calcul Scientifique, Moulay Ismail University)

  • Delfim F. M. Torres

    (University of Aveiro, Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics)

Abstract

We prove boundary inequalities in arbitrary bounded Lipschitz domains on the trace space of Sobolev spaces. For that, we make use of the trace operator, its Moore–Penrose inverse, and of a special inner product. We show that our trace inequalities are particularly useful to prove harmonic inequalities, which serve as powerful tools to characterize the harmonic functions on Sobolev spaces of non-integer order.

Suggested Citation

  • Soumia Touhami & Abdellatif Chaira & Delfim F. M. Torres, 2019. "Harmonic and Trace Inequalities in Lipschitz Domains," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 599-611, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_30
    DOI: 10.1007/978-3-030-28950-8_30
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