Corpus ID: 119264852

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}
}
  • A. Castro, S. Rodríguez-López, W. Staubach
  • Published 2015
  • Mathematics
  • arXiv: Analysis of PDEs
  • 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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