Douglas N. Arnold ¹, Patrick J. Noon ¹

The single layer heat potential optential operator, K, arises in the solution of initialboundary 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 covercivity inequality $ ‹ K_{q,q} ›\geq c\|q\|^2$. We thereby establish the well-posedness of the operator equation $K_q=f$ and provide a basis for the analysis of the discretizations.

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