Harmonic and Trace Inequalities in Lipschitz Domains

Soumia Touhami (), Abdellatif Chaira () and Delfim F. M. Torres ()
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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

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 599-611 from Springer

Abstract: 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.

Keywords: Moore–Penrose equality; Trace inequalities; Harmonic inequalities; Lipschitz domains; Trace spaces; Harmonic functions; Hilbert spaces; 47A30; 47J20 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-28950-8_30

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DOI: 10.1007/978-3-030-28950-8_30

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