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Sur l’unicité du problème de Cauchy et le prolongement unique pour des équations elliptiques à coefficients non localement bornes. (French) Zbl 0431.35017

MSC:
35B60 Continuation and prolongation of solutions to PDEs
35J15 Second-order elliptic equations
35J30 Higher-order elliptic equations
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[1] Agmon, S; Douglis, A; Nirenberg, L, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Comm. pure appl. math., 17, 35-92, (1964) · Zbl 0123.28706
[2] \scW. O. Amrein, A. M. Berthier, et V. Georgescu, An Lp inequality for the laplacien and unique continuation, à paraître. · Zbl 0468.35017
[3] Aronszajn, N, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. math. pures appl., 36, 235-249, (1957) · Zbl 0084.30402
[4] Berthier, A.M, Sur le spectre ponctuel de l’opérateur de Schrödinger, C.R. acad. sci. Paris, 290, 393-395, (1980) · Zbl 0454.35070
[5] Carleman, T, Sur un problème d’unicité pour LES systèmes d’équations aux dérivées partielles à deux variables indépendantes, Ark. mat. astr. fys., 26B, n∘ 17, 1-9, (1939) · Zbl 0022.34201
[6] Cohen, P, The non-uniqueness of the Cauchy problem, Office of naval research technical report 93, (1960), Stanford
[7] Georgescu, V, Helv. phys. acta, (1980)
[8] Goorjian, P.M, The uniqueness of the Cauchy problem for partial differential equations which may have multiple characteristics, Trans. amer. math. soc., 146, 493-509, (1969) · Zbl 0188.41502
[9] Grubb, G, Boundary problems for systems of partial differential operators of mixed order, J. funct. anal., 26, 131-165, (1977) · Zbl 0368.35030
[10] Grubb, G; Geymonat, G, The essential spectrum of elliptic systems of mixed order, Math. ann., 227, 247-276, (1977) · Zbl 0361.35050
[11] Heinz, E, Über die eindentigkeit beim cauchyschen anfangswertproblem einer elliptischen differentialgleichung zweiter ordnung, Nachr. akad. wiss. Göttingen math.-phys., kl. iia, n∘ 1, 1-12, (1955) · Zbl 0067.07503
[12] Hörmander, L, Linear partial differential operators, (1969), Springer-Verlag Berlin/Heidelberg/New York · Zbl 0177.36401
[13] Hörmander, L, On the uniqueness of the Cauchy problem, II, Math. scand., 7, 177-190, (1955) · Zbl 0090.08001
[14] Hörmander, L, Pseudo-differential operators and non elliptic boundary problems, Ann. of math., 83, 129-209, (1966) · Zbl 0132.07402
[15] Mizohata, S, Unicité du prolongement des solutions des équations elliptiques du quatrième ordre, (), 687-692 · Zbl 0085.08501
[16] Müller, C, On the behaviour of the solutions of the differential equation δu = F(x, u) in the neighbourhood of a point, Comm. pure appl. math., 7, 505-515, (1954) · Zbl 0056.32201
[17] Nirenberg, L, Uniqueness in Cauchy problems for differential equations with constant leading coefficients, Comm. pure appl. math., 10, 89-105, (1957) · Zbl 0077.09402
[18] Pederson, R, On the unique continuation theorem for certain second and fourth order elliptic equations, Comm. pure appl. math., 11, 67-80, (1958) · Zbl 0080.30703
[19] Pederson, R, Uniqueness in Cauchy’s problem for elliptic equations with double characteristics, Ark. mat., 6, 535-549, (1966) · Zbl 0146.34201
[20] Plis, A, A smooth linear elliptic differential equation without any solution in a sphere, Comm. pure appl. math., 14, 599-617, (1968) · Zbl 0163.13103
[21] Plis, A, On non-uniqueness in Cauchy problem for an elliptic second order differential equation, Bull. acad. polon. sci. Sér. sci. math. astronom. phys., 11, n∘ 3, 95-100, (1963) · Zbl 0107.07901
[22] Reed, M; Simon, B, Methods of modern mathematical physics, IV, analysis of operators, (1978), Academic Press New York · Zbl 0401.47001
[23] Saut, J.C; Scheurer, B, Un théorème de prolongement unique pour des opérateurs elliptiques dont LES coefficients ne sont pas localement bornés, C.R. acad. sci. Paris Sér. A, 290, 595-598, (1980) · Zbl 0429.35020
[24] Saut, J.C; Temam, R, Generic properties of Navier-Stokes equations: genericity with respect to the boundary values, Indiana J. math., (1980) · Zbl 0445.76023
[25] Saut, J.C; Temam, R, Generic properties of nonlinear boundary value problem, Comm. partial differential equations, 4, n∘ 3, 293-319, (1979) · Zbl 0462.35016
[26] \scM. Schechter et B. Simon, Unique continuation for Schrödinger operators with unbounded potentials, J. Math. Anal. Appl., in press.
[27] Sussman, M.M, On uniqueness in Cauchy’s problem for elliptic partial differential operators with characteristics of multiplicity greater than two, Tôhoku math. J., 29, 165-188, (1977) · Zbl 0355.35028
[28] Watanabe, K, On the uniqueness of the Cauchy problem for certain elliptic equations with triple characteristics, Tôhoku math. J., 23, 473-490, (1971) · Zbl 0237.35032
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