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Convexity and uniqueness in an inverse problem of potential theory

Author: Henrik Shahgholian
Journal: Proc. Amer. Math. Soc. 116 (1992), 1097-1100
MSC: Primary 31B20
MathSciNet review: 1137234
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Abstract: Let $ {\Omega _1}$ and $ {\Omega _2}$ be two bounded domains in $ {\mathbb{R}^n}$ whose intersection is convex. Suppose moreover that their volume potentials coincide in the complement of their union. Then $ {\Omega _1} = {\Omega _2}$.

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

  • [1] L. A. Caffarelli, Compactness methods in free boundary problems, Partial Differential Equations 5 (1980), 427-448. MR 567780 (81e:35121)
  • [2] E. Hopf, A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc. 3 (1952), 791-793. MR 0050126 (14:280b)
  • [3] V. Isakov, Inverse source problems, Math. Surveys Monographs, vol. 34, Amer. Math. Soc., Providence, RI, 1990. MR 1071181 (92g:35230)
  • [4] P. S. Novikov, Sur le probème inverse du potentiel, Dokl. Akad. Nauk SSSR 18 (1938), 165-168.
  • [5] L. Zalcman, Some inverse problems of potential theory, Contemp. Math., vol. 63, Amer. Math. Soc., Providence, RI, 1987, pp. 337-350. MR 876329 (88e:31012)

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Keywords: Convexity, volume potential, inverse problem
Article copyright: © Copyright 1992 American Mathematical Society

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