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

Robert Beals, Michael Reed

Research output: Contribution to journalArticle

27 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)159-184
Number of pages26
JournalTransactions of the American Mathematical Society
Volume285
Issue number1
DOIs
StatePublished - Jan 1 1984

Fingerprint

Pseudodifferential Operators
Linear equations
Partial differential equations
Nonlinear Problem
Calculus
Regularity
Regularity of Solutions
Regularity Properties
Theorem
Linear equation
Partial differential equation
Coefficient

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematics(all)

Cite this

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Microlocal regularity theorems for nonsmooth pseudodifferential operators and applications to nonlinear problems. / Beals, Robert; Reed, Michael.

In: Transactions of the American Mathematical Society, Vol. 285, No. 1, 01.01.1984, p. 159-184.

Research output: Contribution to journalArticle

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