A Trace Theorem for Solutions of Linear Partial Differential Equations

Abstract

This paper proves a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions. the trace of the solution on a codimension one hypersurface will be just as regular as the solution itself. The proof is based on the Hoermander-Nirenberg pseudo-differential cut-off technique and a "fattening" lemma, together with standard energy estimates.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1989
Accession Number
ADA455263

Entities

People

  • Gang Bao
  • William W. Symes

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Information Operations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Real Variables
  • Standards

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.