Maximal regularity of type L
p
for abstract parabolic Volterra equations |
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Authors: | Rico Zacher |
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Institution: | (1) Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, D-06120 Halle (Saale), Germany |
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Abstract: | We prove maximal regularity results of type Lp for abstract parabolic Volterra equations including problems with inhomogeneous boundary data. Our approach is purely operator theoretic. It uses the inversion of the convolution, the Dore-Venni theorem, the Mikhlin theorem in the operator-valued version, and real interpolation. Known results on Lp-regularity of abstract Cauchy problems and abstract parabolic pde s with inhomogeneous boundary conditions are recovered. As an application we consider the heat equation of memory type with inhomogeneous boundary condition. |
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Keywords: | 45D05 45N05 45K05 |
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