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Regularity Properties of Generalized Analytic Vectors in Rn

✍ Scribed by Bernd Goldschmidt

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
335 KB
Volume
103
Category
Article
ISSN
0025-584X

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✦ Synopsis

The aim of this paper is to describe regularity properties of the solutions of a certain class of first order elliptic systems of partial differential equations in the EucLIDian space R". These systems have many important applications in mathematical physics (for instance equations in elasticity, MAXWELL'S equations in the stationary case, etc). In this paper we use a CLIFFORD algebra& to represent these systems. When the systems are homogeneous consisting only of a principal part then there function theoretic properties have been examined by many authors [4], [6], [9], [lo], [ I l l , [13]. To study general linear systems of partial differential equations with the same principal part we require results on the regularity of weak solutions of such systems. Weaker results have been obtained earlier by AGMON, DOUGLIS and NIRENBERG [l], [ 5 ] .

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