Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425617 | Advances in Mathematics | 2015 | 51 Pages |
Abstract
Let P be a classical pseudodifferential operator of order mâC on an n-dimensional Câ manifold Ω1. For the truncation PΩ to a smooth subset Ω there is a well-known theory of boundary value problems when PΩ has the transmission property (preserves Câ(Ω¯)) and is of integer order; the calculus of Boutet de Monvel. Many interesting operators, such as for example complex powers of the Laplacian (âÎ)μ with μâZ, are not covered. They have instead the μ-transmission property defined in Hörmander's books, mapping xnμCâ(Ω¯) into Câ(Ω¯). In an unpublished lecture note from 1965, Hörmander described an L2-solvability theory for μ-transmission operators, departing from Vishik and Eskin's results. We here develop the theory in Lp Sobolev spaces (1
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Gerd Grubb,