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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0887494-0

MathSciNet review:
887494

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Abstract: Let be domains in . For each we are given a system of linear constant coefficient operators and a function on satisfying . When the satisfy certain compatibility conditions on the intersections then we can extend them so as to be solutions of 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

DOI:
https://doi.org/10.1090/S0002-9947-1987-0887494-0

Keywords:
Reflection,
removable singularities,
Hartogs theorem,
Lewy theorem

Article copyright:
© Copyright 1987
American Mathematical Society