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Unique continuation for elliptic equations


Author: M. H. Protter
Journal: Trans. Amer. Math. Soc. 95 (1960), 81-91
MSC: Primary 35.00
DOI: https://doi.org/10.1090/S0002-9947-1960-0113030-3
MathSciNet review: 0113030
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  • [1] N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) vol. 36 (1957) pp. 235-249. MR 0092067 (19:1056c)
  • [2a] L. Bers, (a) Theory of pseudoanalytic functions, New York, New York University, 1953.
  • [2b] -(b) Local behavior of general elliptic equations, Comm. Pure Appl. Math. vol. 8 (1955) pp. 473-496. MR 0075416 (17:743a)
  • [3] A. P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. vol. 80 (1958) pp. 16-36. MR 0104925 (21:3675)
  • [4] T. Carleman, Sur les systèmes linéaires aux derivées partielles du premier ordre a deux variables, C. R. Acad. Sci. Paris vol. 197 (1933) pp. 471-474.
  • [5] H. O. Cordes, Über die Bestimmtheit der Lösungen Elliptischer Differentialgleichungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa (1956) pp. 239-258. MR 0086237 (19:148a)
  • [6] A. Douglis, Uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math. vol. 6 (1953) pp. 291-298. MR 0064278 (16:257d)
  • [7] A. Friedman, Uniqueness properties in the theory of differential operators of elliptic type, J. Math. Mech. vol. 7 (1958) pp. 61-67. MR 0093651 (20:174)
  • [8] P. Hartman and A. Wintner, On the local behavior of solutions of non-parabolic partial differential equations, Amer. J. Math. vol. 77 (1955) pp. 453-483. MR 0076156 (17:855a)
  • [9] E. Heinz, Über die Eindentigkeit beim Cauchyschen Anfangswertproblem eines elliptischen Differentialgleichung zweiter Ordnung, Nachr. Akad. Wiss. Göttingen Math-Phys. Kl. IIa (1955) pp. 1-12. MR 0074666 (17:626c)
  • [10] L. Hörmander, On the uniqueness of the Cauchy problem, mimeographed.
  • [11] P. Lax, A stability theorem for solutions of abstract differential equations and its applica tion to the study of the local behavior of solutions of elliptic equations, Comm. Pure Appl. Math. vol. 9 (1956) pp. 747-766. MR 0086991 (19:281a)
  • [12a] S. Mizohata, (a) Unicité dans le problème de Cauchy pour quelques équations différentielles elliptiques, Mem. Coll. Sci. Univ. Kyoto ser. A vol. 31 (1958) pp. 121-128. MR 0103347 (21:2119)
  • [12b] -(b) Unicité du prolongement des solutions des équations elliptiques du quatrième ordre, Proc. Japan Acad. vol. 34 (1958) pp. 687-692. MR 0105553 (21:4292)
  • [13] C. Muller, On the behavior of the solutions of the differential equation $ \Delta u = F(x,u)$ in the neighborhood of a point, Comm. Pure Appl. Math. vol. 7 (1954) pp. 505-551. MR 0062920 (16:42c)
  • [14] L. Nirenberg, Uniqueness in Cauchy problems for differential equations with constant leading coefficients, Comm. Pure Appl. Math. vol. 10 (1957) pp. 89-105. MR 0086232 (19:147a)
  • [15] R. N. Pederson, On the unique continuation theorem for certain second and fourth order equations, Comm. Pure Appl. Math. vol. 11 (1958) pp. 67-80. MR 0098900 (20:5350)

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DOI: https://doi.org/10.1090/S0002-9947-1960-0113030-3
Article copyright: © Copyright 1960 American Mathematical Society

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