Boundary value problems for first order elliptic wedge operators

Thomas Krainer, Gerardo A. Mendoza

Research output: Contribution to journalArticle

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Abstract

We develop an elliptic theory based in L2 of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be constant along the base of the boundary fibration. Our theory includes as a special case the classical theory of elliptic boundary value problems for first order operators with and without the Shapiro-Lopatinskii condition, and can be thought of as a natural extension of that theory to the geometrically and analytically relevant class of wedge operators. Wedge operators arise in the global analysis on manifolds with incomplete edge singularities. Our theory settles, in the first order case, the long-standing open problem to develop a robust elliptic theory of boundary value problems for such operators.

Original languageEnglish (US)
Pages (from-to)585-656
Number of pages72
JournalAmerican Journal of Mathematics
Volume138
Issue number3
DOIs
Publication statusPublished - Jun 2016

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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