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Journal Articles Mathematical News / Mathematische Nachrichten Year : 2016

Maximal regularity for non-autonomous Robin boundary conditions

Wolfgang Arendt
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Sylvie Monniaux
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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 Hölder 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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Dates and versions

hal-01073811 , version 1 (10-10-2014)
hal-01073811 , version 2 (05-03-2015)



Wolfgang Arendt, Sylvie Monniaux. Maximal regularity for non-autonomous Robin boundary conditions. Mathematical News / Mathematische Nachrichten, 2016, 283 (11-12), pp.1325-1340. ⟨hal-01073811v2⟩
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