The Friedrichs extension for elliptic wedge operators of second order

Thomas Krainer, Gerardo A. Mendoza

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let M be a smooth compact manifold whose boundary is the total space of a fibration N → Y with compact fibers, let E → M be a vector bundle. Let be a second order elliptic semibounded wedge operator. Under certain mild natural conditions on the indicial and normal families of A, the trace bundle of A relative to ν splits as a direct sum I = IF ⊕ IaF and there is a natural map P: C(Y;IF) → C(M; E) such that CIF(M; E) = P(C(Y;IF)) + Ċ(M;E) ⊂ Dmax(A). It is shown that the closure of A when given the domain CIF(M;E) is the Friedrichs extension of (†) and that this extension is a Fredholm operator with compact resolvent. Also given are theorems pertaining the structure of the domain of the extension which completely characterize the regularity of its elements at the boundary.

Original languageEnglish (US)
Pages (from-to)295-328
Number of pages34
JournalAdvances in Differential Equations
Volume23
Issue number3-4
StatePublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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