Reflection, removable singularities, and approximation for partial differential equations. II
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- by Leon Ehrenpreis PDF
- Trans. Amer. Math. Soc. 302 (1987), 1-45 Request permission
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
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 1-45
- MSC: Primary 35Bxx; Secondary 32A07, 35E20
- DOI: https://doi.org/10.1090/S0002-9947-1987-0887494-0
- MathSciNet review: 887494