New results on maximal $L^p$-regularity of a class of integrodifferential equations

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2025年1月24日

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H. Bounit,
S. Hadd,
Y. Manar

摘要

The aim of this study is twofold. Initially, by employing a perturbation semigroup approach and admissible observation operators, a novel variation of constants formula is presented for the mild solutions of a specific set of integrodifferential equations in Banach spaces. Subsequently, utilizing this formula, an examination of the maximal $L^p$ $L^{p}$ -regularity for such equations is conducted through the application of the sum operator method established by Da Prato and Grisvard. Importantly, it is demonstrated that the maximal $L^p$ $L^{p}$ -regularity of an integrodifferential equation is equivalent to that of the same equation when the integral term is omitted. Furthermore, a finding concerning the strong solution of an initial value integrodifferential equation is provided when the initial condition pertains to the trace space.

New results on maximal \(L^p\)-regularity of a class of integrodifferential equations

摘要