Estimates for evolutionary partial differential equations in classical function spaces

Alejandro Castro Castilla, Anders Israelsson, Wolfgang Staubach, Madi Yerlanov

Research output: Contribution to journalArticlepeer-review

Abstract

We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations. More specifically, we obtain optimal (local in time) estimates for the solution to the Cauchy problem for variable-coefficient evolutionary partial differential equations. The estimates are achieved by introducing the notions of Schrödinger and general oscillatory integral operators with inhomogeneous phase functions and prove sharp local and global regularity results for these in Besov–Lipschitz and Triebel–Lizorkin spaces.
Original languageEnglish
Pages (from-to)1-57
JournalForum of Mathematics, Sigma
Volume11
DOIs
Publication statusPublished - 2023

Keywords

  • Schrödinger integral operators
  • Oscillatory integral operators

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