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Summary: COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL
by
Douglas N. Arnold and Patrick J. Noon
Department of Mathematics
University of Maryland
College Park, MD 20742
USA
Abstract. The single layer heat potential operator, K, arises in the solution of initial-
boundary value problems for the heat equation using boundary integral methods. In this note
we show that K maps a certain anisotropic Sobolev space isomorphically onto its dual, and,
moreover, satisfies the coercivity inequality Kq, q c q 2
. We thereby establish the well-
posedness of the operator equation Kq = f and provide a basis for the analysis of the
discretizations.
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§1. Introduction
If u(x, t) solves the homogeneous heat equation for x in a smoothly bounded domain
in R3
and t > 0 and vanishes when t = 0, then u may be expressed in terms of its Cauchy
data on × R+ as
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