AbstractHere we consider initial boundary value problems for the heat equation by using the heat potential representation for the solution. Depending on the choice of the representation we are led to a solution of the various boundary integral equations. We discuss the solvability of these equations in anisotropic Sobolev spaces. It turns out that the double‐layer heat potentialDand its spatial adjointD′ have smoothing properties similar to the single‐layer heat operator. This yields compactness of the operatorsDandD′. In addition, for any constantc≠ 0,cI+D′ andcI+D′ are isomorphisms. Based on the coercivity of the single‐layer heat operator and the above compactness we establish the coerciveness of the hypersingular heat operator. Moreover, we show an equivalence between the weak solution and the various boundary integral solutions. As a further application we describe a coupling procedure for an exterior initial boundary value problem for the non‐homogene
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