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Operational approach for biharmonic equations in \({\varvec{L}}^{{\varvec{p}}}\)-spaces

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Abstract

In this work, we study the existence, uniqueness and maximal \(L^p\)-regularity of the solution of different biharmonic problems. We rewrite these problems by a fourth-order operational equation and different boundary conditions, set in a cylindrical n-dimensional spatial region \(\Omega \) of \({\mathbb {R}}^n\). To this end, we give an explicit representation formula, using analytic semigroups, and invert explicitly a determinant operator in \(L^p\)-spaces thanks to \(\mathcal {E}_\infty \) functional calculus and operator sums theory.

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Acknowledgements

This research is supported by CIFRE Contract 2014/1307 with Qualiom Eco company. The author would like to thank the referee for the valuable and useful comments and corrections which help to improve this paper.

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  1. UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, Normandie Univ, 76600, Le Havre, France

    Alexandre Thorel

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  1. Alexandre Thorel
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Correspondence to Alexandre Thorel.

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Thorel, A. Operational approach for biharmonic equations in \({\varvec{L}}^{{\varvec{p}}}\)-spaces. J. Evol. Equ. 20, 631–657 (2020). https://doi.org/10.1007/s00028-019-00536-2

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