Approximate solutions of vector fields and an application to Denjoy–Carleman regularity of solutions of a nonlinear PDE

Nicholas Braun Rodrigues*, Antonio Victor da Silva

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study microlocal regularity of a (Formula presented.) -solution u of the equation (Formula presented.) where (Formula presented.) is ultradifferentiable in the variables (Formula presented.) and holomorphic in the variables (Formula presented.). We proved that if (Formula presented.) is a regular Denjoy–Carleman class (including the quasianalytic case) then: (Formula presented.) where (Formula presented.) is the Denjoy–Carleman wave-front set of u and (Formula presented.) is the characteristic set of the linearized operator (Formula presented.) : (Formula presented.)

Original languageEnglish
Pages (from-to)1452-1471
Number of pages20
JournalMathematische Nachrichten
Volume294
Issue number8
DOIs
Publication statusPublished - Aug 2021
Externally publishedYes

Keywords

  • Denjoy–Carleman approximate solutions
  • Denjoy–Carleman wave-front set
  • quasianalytic classes

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