Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Unique continuation for elliptic equations

Author: M. H. Protter
Journal: Trans. Amer. Math. Soc. 95 (1960), 81-91
MSC: Primary 35.00
MathSciNet review: 0113030
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235–249. MR 0092067 (19,1056c)
  • [2a] L. Bers, (a) Theory of pseudoanalytic functions, New York, New York University, 1953.
  • [2b] Lipman Bers, Local behavior of solutions of general linear elliptic equations, Comm. Pure Appl. Math. 8 (1955), 473–496. MR 0075416 (17,743a)
  • [3] A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations., Amer. J. Math. 80 (1958), 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 eindeutige Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa. 1956 (1956), 239–258 (German). MR 0086237 (19,148a)
  • [6] Avron Douglis, Uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math. 6 (1953), 291–298. MR 0064278 (16,257d)
  • [7] Avner Friedman, Uniqueness properties in the theory of differential operators of elliptic type, J. Math. Mech. 7 (1958), 61–67. MR 0093651 (20 #174)
  • [8] Philip Hartman and Aurel Wintner, On the local behavior of solutions of non-parabolic partial differential equations. III. Approximations by spherical harmonics, Amer. J. Math. 77 (1955), 453–474. MR 0076156 (17,855a)
  • [9] Erhard Heinz, Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung, Nachr. Akad. Wiss. Göttingen. IIa. 1955 (1955), 1–12 (German). MR 0074666 (17,626c)
  • [10] L. Hörmander, On the uniqueness of the Cauchy problem, mimeographed.
  • [11] P. D. Lax, A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations, Comm. Pure Appl. Math. 9 (1956), 747–766. MR 0086991 (19,281a)
  • [12a] Sigeru Mizohata, Unicité dans le problème de Cauchy pour quelques équations différentielles elliptiques, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 31 (1958), 121–128 (French). MR 0103347 (21 #2119)
  • [12b] Sigeru Mizohata, Unicité du prolongement des solutions des équations elliptiques du quatrième ordre, Proc. Japan Acad. 34 (1958), 687–692 (French). MR 0105553 (21 #4292)
  • [13] Claus Müller, On the behavior of the solutions of the differential equation Δ𝑈=𝐹(𝑥,𝑈) in the neighborhood of a point, Comm. Pure Appl. Math. 7 (1954), 505–515. MR 0062920 (16,42c)
  • [14] Louis Nirenberg, Uniqueness in Cauchy problems for differential equations with constant leading coefficients, Comm. Pure Appl. Math. 10 (1957), 89–105. MR 0086232 (19,147a)
  • [15] R. N. Pederson, On the unique continuation theorem for certain second and fourth order elliptic equations, Comm. Pure Appl. Math. 11 (1958), 67–80. MR 0098900 (20 #5350)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35.00

Retrieve articles in all journals with MSC: 35.00

Additional Information

PII: S 0002-9947(1960)0113030-3
Article copyright: © Copyright 1960 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia