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Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems
Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Faculty of Science, Department of Mathematics. matematik.
2008 (English)In: Journal of functional analysis, ISSN 0022-1236, Vol. 255, no 2, 374-448 p.Article in journal (Refereed) Published
Abstract [en]

We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a new boundary operator method which makes use of operators in the functional calculus of an underlaying first order Dirac type operator. We establish quadratic estimates for this Dirac operator, which implies that the associated Hardy projection operators are bounded and depend continuously on the coefficient matrix. We also prove that certain transmission problems for $k$-forms are well posed for small perturbations of block matrices.

Place, publisher, year, edition, pages
2008. Vol. 255, no 2, 374-448 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:su:diva-20727ISI: 000256739300003OAI: oai:DiVA.org:su-20727DiVA: diva2:187253
Available from: 2008-11-06 Created: 2008-11-06 Last updated: 2011-01-10Bibliographically approved

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http://arxiv.org/abs/0705.0250

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