References
S. Alinhac, Non-unicité pour des opérateurs différentiels à caracteristiques complexes simples, Ann. Sci. Ecole Norm. Sup. 13 (1980), 385–393.
B. Barcelo, C. Kenig, A. Ruiz, C. Sogge, Unique continuation properties for solutions of inequalities between the Laplacean and the gradient, Ill. J. Math. 32(2) (1988), 230–245.
L. Brown, Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory, Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol. 9, (1986).
A.P. Calderon, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36.
C. Fefferman, The multiplier problem for the ball, Ann. Math. 94 (1971), 330–336.
L. Hormander, On the uniqueness of the Cauchy problem, Math. Scand. 6 (1958), 213–225.
L. Hormander, On the uniqueness of the Cauchy problem II, Math. Scand. 7 (1959), 177–190.
L. Hormander, Uniqueness theorem for second order elliptic differential operators, Comm. PDE 8 (1983), 21–64.
D. Jerison, Carleman inequalities for the Dirac and Laplace operator and unique continuation, Adv. Math. 62 (1986), 118–134.
D. Jerison, C. Kenig, Unique continuation and absence of positive eigenvalues for Schrodinger operators, with an appendix by E.M. Stein, Ann. Math. 121 (1985), 463–494.
C. Kenig, A. Ruiz, C. Sogge, Remarks on unique continuation problems, Seminarios, Universidad Autonoma de Madrid, 1986.
C. Kenig, A. Ruiz, C. Sogge, Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), 329–347.
L. Nirenberg, Lectures on Linear Partial Differential Equations, Regional conference series in mathematics 17, Amer. Math. Soc. 1973.
G. Pisier, The Volume of Convex Sets and Banach Space Geometry, Cambridge University Press, 1989.
A. Plis, On nonuniqueness in Cauchy problems for an elliptic second order differential operator, Bull. Acad. Polon. Sci. 11 (1963), 95–100.
M. Schechter, B. Simon, Unique continuation for Schrodinger operators with unbounded potential, J. Math. Anal. Appl. 77 (1980), 482–492.
C. Sogge, Oscillatory integrals and unique continuation for second order elliptic differential equations, J. Amer. Math. Soc. 2 (1989), 489–515.
C. Sogge, Strong uniqueness theorem for second order elliptic differential equations, Amer. J. Math. 112 (1990), 943–984.
V.M. Tikhomirov, Convex Analysis, in Encyclopedia of Mathematical Sciences 14: Analysis 2 (ed. M. Gamkrelidze), Springer Verlag 1990.
T. Wolff, Unique continuation for |Δu|≤V|∇|u| and related problems, Revista Math. Iberoamericana 6:3–4 (1990), 155–200.
C. Zuily, Uniqueness and Non-uniqueness in the Cauchy Problem, Birkhäuser, Boston, 1983.
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Wolff, T.H. A property of measures inR N and an application to unique continuation. Geometric and Functional Analysis 2, 225–284 (1992). https://doi.org/10.1007/BF01896975
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DOI: https://doi.org/10.1007/BF01896975