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The Global Cauchy Problem for the Plate Equation in Weighted Sobolev Spaces

  • Alessia AscanelliEmail author
Chapter
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Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We consider the initial value problem for the plate equation with (t, x) −depending complex valued lower order terms. Under suitable decay conditions as |x|→ on the imaginary part of the subprincipal term we prove energy estimates in weighted Sobolev spaces. This provides also well posedness of the Cauchy problem in the Schwartz space \(\mathcal {S}(\mathbb R^n)\) and in \(\mathcal {S}^\prime (\mathbb R^n)\).

Keywords

Plate equation Weighted Sobolev spaces Pseudodifferential operators 

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità degli studi di FerraraFerraraItaly

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