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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Michael Beals and Michael Reed
Journal: Trans. Amer. Math. Soc. 285 (1984), 159-184
MSC: Primary 35S05; Secondary 35J60, 35L70
MathSciNet review: 748836
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0748836-7
PII: S 0002-9947(1984)0748836-7
Article copyright: © Copyright 1984 American Mathematical Society