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

DOI:
https://doi.org/10.1090/S0002-9939-1992-1137234-2

MathSciNet review:
1137234

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be two bounded domains in whose intersection is convex. Suppose moreover that their volume potentials coincide in the complement of their union. Then .

**[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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1137234-2

Keywords:
Convexity,
volume potential,
inverse problem

Article copyright:
© Copyright 1992
American Mathematical Society