Edge Sobolev spaces and weakly hyperbolic equations |
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| Authors: | Michael Dreher Ingo Witt |
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| Affiliation: | (1) Institute of Mathematics, University of Tsukuba, Tsukuba–shi, Ibaraki 305, Japan, e-mail: dreher@math.tsukuba.ac.jp, JP;(2) Institute of Mathematics, University of Potsdam, PF 60 15 53, D-14415 Potsdam, Germany, e-mail: ingo@math.uni-potsdam.de, DE |
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| Abstract: | Summary. Edge Sobolev spaces are proposed as a main new tool for the investigation of weakly hyperbolic equations. The well-posedness of the linear and semilinear Cauchy problem in the class of these edge Sobolev spaces is proved. An application to the propagation of singularities for solutions to the semilinear problem is considered. Received: October 3, 2000 Published online: December 19, 2001 |
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| Keywords: | Mathematics Subject Classification (2000). Primary: 35L80 Secondary: 46E35, 35L15 |
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