Abstract.
We prove maximal regularity results of type L p 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 L p -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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Zacher, R. Maximal regularity of type L p for abstract parabolic Volterra equations. J. evol. equ. 5, 79–103 (2005). https://doi.org/10.1007/s00028-004-0161-z
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DOI: https://doi.org/10.1007/s00028-004-0161-z