The method of layer potentials in Lp and endpoint spaces for elliptic operators with L coefficients

Steve Hofmann, Marius Mitrea, Andrew Morris

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)
141 Downloads (Pure)

Abstract

We consider layer potentials associated to elliptic operators Lu=−div(A∇u) acting in the upper half-space Rn+1+ for n≥2, or more generally, in a Lipschitz graph domain, where the coefficient matrix A is L- and t-independent, and solutions of Lu=0 satisfy interior estimates of De Giorgi/Nash/Moser type. A ‘Calderón–Zygmund’ theory is developed for the boundedness of layer potentials, whereby sharp Lp and endpoint space bounds are deduced from L2-bounds. Appropriate versions of the classical ‘jump relation’ formulae are also derived. The method of layer potentials is then used to establish well-posedness of boundary value problems for L with data in Lp and endpoint spaces.
Original languageEnglish
Pages (from-to)681-716
Number of pages36
JournalLondon Mathematical Society. Proceedings
Volume111
Issue number3
Early online date12 Aug 2015
DOIs
Publication statusPublished - 1 Sep 2015

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