# Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with Hölder continuous coefficients

@article{Castro2015SolvabilityOT, title={Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with H{\"o}lder continuous coefficients}, author={A. Castro and S. Rodr{\'i}guez-L{\'o}pez and W. Staubach}, journal={arXiv: Analysis of PDEs}, year={2015} }

We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with H\"older-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.

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