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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
DOI: https://doi.org/10.1090/S0002-9947-1969-0239253-9
MathSciNet review: 0239253
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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. 36 (1957), 235-249. MR 0092067 (19:1056c)
  • [2] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Atti del convegno internazionale sulle equazione alle derivate parzialli, Trieste, 1954, pp. 111-140. MR 0076981 (17:974d)
  • [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. Cordes, Über die eindeutige Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa (1956), 239-258. MR 0086237 (19:148a)
  • [6] J. Douglas, Jr., ``Approximate continuation of harmonic and parabolic functions,'' in Numerical solution of partial differential equations, J. H. Bramble (editor), Academic Press, New York, 1966. MR 0202333 (34:2206)
  • [7] -, ``A numerical method for analytic continuation,'' in Boundary problems in differential equations, R. E. Langer (editor), Univ. of Wisconsin Press, Madison, 1960. MR 0117866 (22:8640)
  • [8] A. Douglis, Uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math. 6 (1953), 291-298; 13 (1960), 593-607. MR 0064278 (16:257d)
  • [9] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 0181836 (31:6062)
  • [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] E. Heinz, Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem eins elliptischen Differentialgleichung zweiter Ordnung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa (1955), 1-12. MR 0074666 (17:626c)
  • [12] E. Hille, Analytic function theory, Vol. II, Ginn, Boston, 1962, p. 410. MR 0201608 (34:1490)
  • [13] L. Hörmander, Linear partial differential operators, Academic Press, New York, 1963.
  • [14] F. John, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math. 13 (1960), 551-585. MR 0130456 (24:A317)
  • [15] E. Landis, A three-spheres theorem, Soviet Math. Dokl. 4 (1963), 76-78. MR 0150445 (27:443)
  • [16] K. Miller, Three circle theorems in partial differential equations and their applications to improperly posed problems, Arch. Rational Mech. Anal. 16 (1964), 126-154. MR 0164136 (29:1435)
  • [17] C. Morrey, Jr., On the analyticity of solutions of analytic non-linear elliptic systems of partial differential equations, Amer. J. Math. 80 (1958), 198-237. MR 0106336 (21:5070)
  • [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. Protter, Unique continuation for elliptic equations, Trans. Amer. Math. Soc. 95 (1960), 81-91. MR 0113030 (22:3871)

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DOI: https://doi.org/10.1090/S0002-9947-1969-0239253-9
Article copyright: © Copyright 1969 American Mathematical Society

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