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2015 Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus
Steve Hofmann, Marius Mitrea, Michael Taylor
Anal. PDE 8(1): 115-181 (2015). DOI: 10.2140/apde.2015.8.115

Abstract

We show that operators of layer potential type on surfaces that are locally graphs of Lipschitz functions with gradients in vmo are equal, modulo compacts, to pseudodifferential operators (with rough symbols), for which a symbol calculus is available. We build further on the calculus of operators whose symbols have coefficients in Lvmo, and apply these results to elliptic boundary problems on domains with such boundaries, which in turn we identify with the class of Lipschitz domains with normals in vmo. This work simultaneously extends and refines classical work of Fabes, Jodeit and Rivière, and also work of Lewis, Salvaggi and Sisto, in the context of C1 surfaces.

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Steve Hofmann. Marius Mitrea. Michael Taylor. "Symbol calculus for operators of layer potential type on Lipschitz surfaces with VMO normals, and related pseudodifferential operator calculus." Anal. PDE 8 (1) 115 - 181, 2015. https://doi.org/10.2140/apde.2015.8.115

Information

Received: 12 March 2014; Accepted: 5 January 2015; Published: 2015
First available in Project Euclid: 28 November 2017

zbMATH: 1317.31012
MathSciNet: MR3336923
Digital Object Identifier: 10.2140/apde.2015.8.115

Subjects:
Primary: 31B10, 35J57, 35S05, 35S15, 42B20
Secondary: 42B37, 45B05, 58J05, 58J32

Rights: Copyright © 2015 Mathematical Sciences Publishers

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