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28th Southeastern-Atlantic Regional Conference on Differential Equations
October 10-11, 2008
University of Arkansas at Little Rock
Little Rock Arkansas, USA

Organizers
Eric R. Kaufmann, Nickolai Kosmatov

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The regularity problem for the Lame system of elastostatics on curvilinear polygons in two dimensions
by
Katharine Ott
University of Kentucky
Coauthors: Irina Mitrea, Warwick Tucker

We establish sharp well-posedness results for the regularity problem for the Lamé system of elastostatics in the class of curvilinear polygons in two dimensions. The key technical ingredient is obtaining invertibility properties for the boundary version of the single layer potential operator S associated with the Lamé system acting from Lp(∂W) onto Lp1(∂W), 1 < p < ∞, whenever W is an infinite sector in two dimension of aperture q ∈ (0, 2p). Our approach relies on Mellin transform techniques employed to analyze the spectrum of the operator ∂t S on Lp(∂W), 1 < p < ∞.

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Date received: September 3, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caww-18.