Maximal regularity for non-autonomous Robin boundary conditions

Wolfgang Arendt; Sylvie Monniaux

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arXiv · 1410.3063

Maximal regularity for non-autonomous Robin boundary conditions

Wolfgang Arendt·Sylvie Monniaux

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Abstract

We consider a non-autonomous Cauchy problem involving linear operators associated with time-dependent forms $a(t;.,.):V\times V\to {\mathbb{C}}$ where $V$ and $H$ are Hilbert spaces such that $V$ is continuously embedded in $H$. We prove $H$-maximal regularity under a new regularity condition on the form $a$ with respect to time; namely H{ö}lder continuity with values in an interpolation space. This result is best suited to treat Robin boundary conditions. The maximal regularity allows one to use fixed point arguments to some non linear parabolic problems with Robin boundary conditions.

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Wolfgang Arendt, Sylvie Monniaux. 2015-03-06. Maximal regularity for non-autonomous Robin boundary conditions. https://arxiv.org/abs/1410.3063

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