Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with Hölder continuous coefficients
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach · arXiv (Cornell University) · 2015
We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with Hölder-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is achieved through the demonstration of invertibility of the relevant layer-potentials which is in turn based on Fredholm theory and a new systematic approach which yields suitable parabolic Rellich-type estimates.