Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems

Beals, Michael; Reed, Michael

doi:10.1090/S0002-9947-1984-0748836-7

Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems
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by Michael Beals and Michael Reed PDF

Trans. Amer. Math. Soc. 285 (1984), 159-184 Request permission

Abstract:

The authors develop a calculus of pseudodifferential operators with nonsmooth coefficients in order to study the regularity of solutions to linear equations $P (x,D) u = f$. The regularity theorems are similar to those of Bony, but the calculus and the methods of proof are quite different. We apply the linear results to study the regularity properties of solutions to quasilinear partial differential equations.

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Striated solutions of semilinear, two speed wave equations

Pseudo-differential operators