𝐿²-solvability of the Dirichlet, Neumann and regularity problems for parabolic equations with time-independent Hölder-continuous coefficients

Abstract

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.