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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Reflection, removable singularities, and approximation for partial differential equations. II

Author: Leon Ehrenpreis
Journal: Trans. Amer. Math. Soc. 302 (1987), 1-45
MSC: Primary 35Bxx; Secondary 32A07, 35E20
MathSciNet review: 887494
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Abstract: Let $ {\Omega ^j}$ be domains in $ {R^n}$. For each $ j$ we are given a system $ {{\mathbf{D}}^j}$ of linear constant coefficient operators and a function $ {f^j}$ on $ {\Omega ^j}$ satisfying $ {{\mathbf{D}}^j}{f^j} = 0$. When the $ {f^j}$ satisfy certain compatibility conditions on the intersections $ {\Omega ^j} \cap {\Omega ^{j'}}$ then we can extend them so as to be solutions of $ {{\mathbf{D}}^j}$ on larger domains. As a consequence of our methods we are able to sharpen Hartogs' theorems to allow for continuation of solutions of overdetermined systems over noncompact sets.

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Additional Information

PII: S 0002-9947(1987)0887494-0
Keywords: Reflection, removable singularities, Hartogs theorem, Lewy theorem
Article copyright: © Copyright 1987 American Mathematical Society