Harmonic and Trace Inequalities in Lipschitz Domains

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.

This is a preprint of a paper accepted 15-Nov-2018 and whose final and definite form is a book chapter at Springer New York, on the topic of 'Frontiers in Functional Equations and Analytic Inequalities', Edited by G. Anastassiou and J. Rassias