Edge Sobolev spaces and weakly hyperbolic equations. (English) Zbl 1223.35240
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.
MSC:
35L80 | Degenerate hyperbolic equations |
46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
35L15 | Initial value problems for second-order hyperbolic equations |