Convexity and uniqueness in an inverse problem of potential theory
HTML articles powered by AMS MathViewer
- by Henrik Shahgholian PDF
- Proc. Amer. Math. Soc. 116 (1992), 1097-1100 Request permission
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
- Luis A. Caffarelli, Compactness methods in free boundary problems, Comm. Partial Differential Equations 5 (1980), no. 4, 427–448. MR 567780, DOI 10.1080/0360530800882144
- Eberhard Hopf, A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc. 3 (1952), 791–793. MR 50126, DOI 10.1090/S0002-9939-1952-0050126-X
- Victor Isakov, Inverse source problems, Mathematical Surveys and Monographs, vol. 34, American Mathematical Society, Providence, RI, 1990. MR 1071181, DOI 10.1090/surv/034 P. S. Novikov, Sur le probème inverse du potentiel, Dokl. Akad. Nauk SSSR 18 (1938), 165-168.
- Lawrence Zalcman, Some inverse problems of potential theory, Integral geometry (Brunswick, Maine, 1984) Contemp. Math., vol. 63, Amer. Math. Soc., Providence, RI, 1987, pp. 337–350. MR 876329, DOI 10.1090/conm/063/876329
Additional Information
- © Copyright 1992 American Mathematical Society
- 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