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$$L^ p-$$inequalities for the Laplacian and unique continuation. (English) Zbl 0468.35017

##### MSC:
 35B60 Continuation and prolongation of solutions to PDEs 35R45 Partial differential inequalities and systems of partial differential inequalities 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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##### References:
 [1] R.A. ADAMS, Sobolev spaces, Academic Press, New York, 1975. · Zbl 0314.46030 [2] A.M. BERTHIER, Sur le spectre ponctuel de l’opérateur de Schrödinger, C.R. Acad. Sci., Paris 290 A, (1980), 393-395 ; On the Point Spectrum of Schrödinger Operators, Ann. Sci. Ecole Normale Supérieure (to appear). · Zbl 0454.35070 [3] N. DUNFORD and J.T. SCHWARTZ, Linear operators, Part I, Interscience, New York, 1957. [4] V. GEORGESCU, On the unique continuation property for Schrödinger Hamiltonians, Helv. Phys. Acta, 52 (1979), 655-670. [5] G.H. HARDY, J.E. LITTELEWOOD and G. POLYA, Inequalities, Cambridge University Press, 1952. · Zbl 0047.05302 [6] E. HEINZ, Über die eindeutigkeit beim Cauchy’schen anfangswert-problem einer elliptischen differentialgleichung zweiter ordnung, Nachr. Akad.-Wiss. Göttingen, II (1955), 1-12. · Zbl 0067.07503 [7] L. HÖRMANDER, Linear partial differential operators, Springer, Berlin, 1963. · Zbl 0108.09301 [8] M. SCHECHTER and B. SIMON, Unique continuation for Schrödinger operators with unbounded potentials, J. Math. Anal. Appl., 77 (1980), 482-492. · Zbl 0458.35024 [9] E.M. STEIN and G. WEISS, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971. · Zbl 0232.42007 [10] H. TRIEBEL, Interpolation theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. · Zbl 0387.46032
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