Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions

@article{Lindemulder2019MaximalRW,
  title={Maximal regularity with weights for parabolic problems with inhomogeneous boundary conditions},
  author={Nick Lindemulder},
  journal={Journal of Evolution Equations},
  year={2019},
  pages={1-50}
}
In this paper, we establish weighted $$L^{q}$$Lq–$$L^{p}$$Lp-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the optimal regularity of the initial-boundary data and allow to avoid compatibility conditions at the boundary. The novelty of the followed approach is the use of weighted anisotropic mixed-norm Banach space… CONTINUE READING

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