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Invertibility Properties of Singular Integral Operators Associated with the Lam, and Stokes Systems on Infinite Sectors in Two Dimensions
Temple Univ, Philadelphia, USA.
Bates Coll, Lewiston, USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2017 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 89, no 2, p. 151-207Article in journal (Refereed) Published
Abstract [en]

In this paper we establish sharp invertibility results for the elastostatics and hydrostatics single and double layer potential type operators acting on , , whenever is an infinite sector in . This analysis is relevant to the layer potential treatment of a variety of boundary value problems for the Lam, system of elastostatics and the Stokes system of hydrostatics in the class of curvilinear polygons in two dimensions, such as the Dirichlet, the Neumann, and the Regularity problems. Mellin transform techniques are used to identify the critical integrability indices for which invertibility of these layer potentials fails. Computer-aided proofs are produced to further study the monotonicity properties of these indices relative to parameters determined by the aperture of the sector and the differential operator in question.

Place, publisher, year, edition, pages
2017. Vol. 89, no 2, p. 151-207
Keywords [en]
Lame system, Stokes system, Mellin transform, Hardy kernel operator, Single layer potential, Double layer potential, Conormal derivative, Pseudo-stress conormal derivative, Infinite sector, Interval analysis, Computer-aided proof, Validated numerics
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-340953DOI: 10.1007/s00020-017-2396-4ISI: 000414072300001OAI: oai:DiVA.org:uu-340953DiVA, id: diva2:1182628
Funder
Swedish Research Council, 2008-7510Available from: 2018-02-14 Created: 2018-02-14 Last updated: 2018-02-14Bibliographically approved

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Tucker, Warwick

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