Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35Bxx, 32A07, 35E20

Retrieve articles in all journals with MSC: 35Bxx, 32A07, 35E20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887494-0
PII: S 0002-9947(1987)0887494-0
Keywords: Reflection, removable singularities, Hartogs theorem, Lewy theorem
Article copyright: © Copyright 1987 American Mathematical Society