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

Michael Beals; Michael Reed

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

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

Michael Beals, Michael Reed

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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.

Original language	English (US)
Pages (from-to)	159-184
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	285
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1984-0748836-7
State	Published - Sep 1984

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1984-0748836-7

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

Abstract

All Science Journal Classification (ASJC) codes

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