On extending solutions to Dirichlet problems across the boundary as solutions
type: Item
instance of: scholarly article
title: On extending solutions to Dirichlet problems across the boundary as solutions
zbMATH Open document ID: 0597.35004
DOI: 10.1215/S0012-7094-85-05229-9
author: Mark Williams
published in: Duke Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: Let P be a second order differential oerator defined on an open manifold \(\tilde M\) and noncharacteristic with respect to the boundary \(\partial M\) of a bounded submanifold M. Suppose P has a real principal symbol having fiber-simple characteristics. Let u be an extendible distribution such that Pu\(\in C^{\infty}(M)\) and \(u|_{\partial M}\in C^{\infty}(\partial M)\). It is shown that near gliding points u can be microlocally extended such that Pu remains smooth.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 58J47
zbMATH DE Number: 3962240
zbMATH Keywords: extending solutions
zbMATH Keywords: second order differential oerator
zbMATH Keywords: real principal symbol
zbMATH Keywords: gliding points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3962240