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2017
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We establish the L 2 L^2 -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent Hölder-continuous diffusion coefficients on bounded Lipschitz domains in R n \mathbb {R}^n . This is achieved through the demonstration of invertibility of the relevant layer potentials, which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.