Realisations of elliptic operators on compact manifolds with boundary

Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of Bär-Ballmann to first order elliptic operators. The space of possible boundary values of elements in the maximal domain is described as a Hilbert space densely sandwiched between two mixed order Sobolev spaces. The description uses Calderón projectors which, in the first order case, is equivalent to results of Bär-Bandara using spectral projectors of an adapted boundary operator. Boundary conditions that induce Fredholm as well as regular realisations, and those that admit higher order regularity, are characterised. In addition, results concerning spectral theory, homotopy invariance of the Fredholm index, and well-posedness for higher order elliptic boundary value problems are proven.

Original languageEnglish
Article number108968
JournalAdvances in Mathematics
Volume420
DOIs
Publication statusPublished - 2023

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • Boundary regularity
  • Calderón projector
  • Elliptic differential operator
  • Fredholm boundary conditions

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