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

Publication
, Journal Article

Beals, M; Reed, M

Published in: Transactions of the American Mathematical Society

January 1, 1984

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. © 1984 American Mathematical Society.

### Duke Scholars

## Published In

Transactions of the American Mathematical Society

## DOI

## ISSN

0002-9947

## Publication Date

January 1, 1984

## Volume

285

## Issue

1

## Start / End Page

159 / 184

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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Chicago

ICMJE

MLA

NLM

Beals, M., & Reed, M. (1984). Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems.

*Transactions of the American Mathematical Society*,*285*(1), 159–184. https://doi.org/10.1090/S0002-9947-1984-0748836-7Beals, M., and M. Reed. “Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems.”

*Transactions of the American Mathematical Society*285, no. 1 (January 1, 1984): 159–84. https://doi.org/10.1090/S0002-9947-1984-0748836-7.Beals M, Reed M. Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems. Transactions of the American Mathematical Society. 1984 Jan 1;285(1):159–84.

Beals, M., and M. Reed. “Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems.”

*Transactions of the American Mathematical Society*, vol. 285, no. 1, Jan. 1984, pp. 159–84.*Scopus*, doi:10.1090/S0002-9947-1984-0748836-7.Beals M, Reed M. Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems. Transactions of the American Mathematical Society. 1984 Jan 1;285(1):159–184.

## Published In

Transactions of the American Mathematical Society

## DOI

## ISSN

0002-9947

## Publication Date

January 1, 1984

## Volume

285

## Issue

1

## Start / End Page

159 / 184

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics