Maximal regularity for non‐autonomous Robin boundary conditions |
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Authors: | Wolfgang Arendt Sylvie Monniaux |
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Institution: | 1. +49 (0)731/5023560+49 (0)731/5023619;2. Institut für Angewandte Analysis, Universit?t Ulm, Ulm, Germany;3. Aix‐Marseille Université, CNRS, Centrale Marseille, Marseille, France |
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Abstract: | We consider a non‐autonomous Cauchy problem where is associated with the form , where V and H are Hilbert spaces such that V is continuously and densely embedded in H. We prove H‐maximal regularity, i.e., the weak solution u is actually in (if and ) under a new regularity condition on the form 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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Keywords: | Non‐autonomous parabolic problems Robin boundary conditions maximal regularity 47D06 35K20 35K90 |
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