On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative

Davide Guidetti

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arXiv · 1807.05913

On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative

Davide Guidetti

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Abstract

We prove two maximal regularity results in spaces of continuous and H\"older continuous functions, for a mixed linear Cauchy-Dirichlet problem with a fractional time derivative $\mathbb{D}_t^\alpha$. This derivative is intended in the sense of Caputo and $\alpha$ is taken in $(0, 2)$. In case $\alpha = 1$, we obtain maximal regularity results for mixed parabolic problems already known in mathematica literature.

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Davide Guidetti. 2018-07-16. On maximal regularity for the Cauchy-Dirichlet mixed parabolic problem with fractional time derivative. https://arxiv.org/abs/1807.05913

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