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COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL

COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL,International Journal of Computer Mathematics,Douglas N. Arnold,Patrick J. Noon

COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL   (Citations: 11)
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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 thatK maps a certain anisotropic Sobolev space isomorphically onto its dual, and, moreover, satises the coercivity inequality hKq;qi ckqk 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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