Characterization of Non-Smooth Pseudodifferential Operators

2015/11/29 by Abels, Helmut, Pfeuffer, Christine · 1 citation
#35S05 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1512.01127

Abstract

Smooth pseudodifferential operators on ℝⁿ can be characterized by their mapping properties between L^p-Sobolev spaces due to Beals and Ueberberg. In applications such a characterization would also be useful in the non-smooth case, for example to show the regularity of solutions of a partial differential equation. Therefore, we will show that every linear operator P, which satisfies some specific continuity assumptions, is a non-smooth pseudodifferential operator of the symbol-class C^τ S^m_1,0(ℝⁿ × ℝⁿ). The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols.

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• Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons

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