Abstract
It is natural to consider the propagation of more restricted types of regularity for solutions to strictly hyperbolic problems on domains with boundary, just as in the case of the interior problem considered in Chapters III and IV. From Theorems 5.11 and 5.13, if u ∈ H loc s (R×Rn+), with s > (n + 2)/2 + m - 2, is a solution to (5.2), microlocal regularity of type Hr for u propagates along reflected families of non-grazing null bicharacteristics for r < 2s - (n + 2)/2 - m + 5/2. The same result holds along (possibly grazing) generalized null bicharacteristics in the case of a second order operator. If one is interested in solutions with singularities for which higher order microlocal regularity is propagated (up to H∞), it is again appropriate to study functions conormal with respect to families of characteristic hypersurfaces.
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© 1989 Birkhäuser Boston
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Beals, M. (1989). Conormal Waves on Domains with Boundary. In: Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems. Progress in Mathematics, vol 130. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4554-4_7
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DOI: https://doi.org/10.1007/978-1-4612-4554-4_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3449-0
Online ISBN: 978-1-4612-4554-4
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