Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A priori estimates for continuation problems for elliptic and principally normal differential equations

Author: Paul E. Saylor
Journal: Trans. Amer. Math. Soc. 139 (1969), 95-108
MSC: Primary 35.19
MathSciNet review: 0239253
Full-text PDF

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
  • [2] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali, Trieste, 1954, Edizioni Cremonese, Roma, 1955, pp. 111–140. MR 0076981
  • [3] L. Bers, F. John and M. Schecter, Partial differential equations, Interscience, New York, 1964.
  • [4] T. Carleman, Sur leS systèmes linéaires aux dérivées partielles du premier ordre a deux variables independentes, C. R. Acad. Sci. Paris 197 (1933), 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
  • [6] Jim Douglas Jr., Approximate continuation of harmonic and parabolic functions, Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965) Academic Press, New York, 1966, pp. 353–364. MR 0202333
  • [7] Jim Douglas Jr., A numerical method for analytic continuation, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, pp. 179–189. MR 0117866
  • [8] Avron Douglis, Uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math. 6 (1953), 291–298. MR 0064278,
  • [9] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
  • [10] Ju. K. Gerasimov, The three-sphere theorem for a class of elliptic equations of high order and a refinement of this theorem for a linear elliptic equation of second order, Amer. Math. Soc. Transl. 72 (1968), 135-162.
  • [11] 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
  • [12] Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Co., Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
  • [13] L. Hörmander, Linear partial differential operators, Academic Press, New York, 1963.
  • [14] Fritz John, Continuous dependence on data for solutions of partial differential equations with a presribed bound, Comm. Pure Appl. Math. 13 (1960), 551–585. MR 0130456,
  • [15] E. M. Landis, A three-spheres theorem, Dokl. Akad. Nauk SSSR 148 (1963), 277–279 (Russian). MR 0150445
  • [16] Keith Miller, Three circle theorems in partial differential equations and applications to improperly posed problems, Arch. Rational Mech. Anal. 16 (1964), 126–154. MR 0164136,
  • [17] Charles B. Morrey Jr., On the analyticity of the solutions of analytic non-linear elliptic systems of partial differential equations. I. Analyticity in the interior., Amer. J. Math. 80 (1958), 198–218. MR 0106336,
  • [18] C. Müller, 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. 7 (1954), 505-551.
  • [19] M. H. Protter, Unique continuation for elliptic equations, Trans. Amer. Math. Soc. 95 (1960), 81–91. MR 0113030,

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35.19

Retrieve articles in all journals with MSC: 35.19

Additional Information

Article copyright: © Copyright 1969 American Mathematical Society