Problème de Dirichlet pour des opérateurs hyperboliques de type positif

Authier, Marc

Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 25 (1971) no. 4, pp. 691-765.

[1] Authier M.: Espaces de Sobolev associés à une seule dérivée partielle. C. R. Ac. Sc. Paris 262 (1966) p. 1158-1161. | MR | Zbl

[2] Authier M.: Sur le problème de Dirichlet pour des operatéurs hyperboliques positifs, dans certains ouverts non bornés, C. R. Ac. Sc. Paris 268 (1969) p. 1386-1389. | MR | Zbl

[3] Bardos C.: Thèse Paris (1969).

[4] Berezanskii Y.M.: Expansions in Eigenfunctions of Selfadjoint operators. A. M. S. Transl. of Math. Monogr. n° 17 - 1968. | MR | Zbl

[4bis] Berezanskii Y.M.: Sur le problème de Dirichlet pour l'équation des cordes vibrantes (en russe). Usp. Mat. Nauk 15 (1960).

[5] Bourgin D.G. - Duffin R.: The Dirichlet problem for the vibrating string equation. Bull A. M. S. 45 (1939) p. 851-859. | MR | Zbl

[5bis] Borman J.: On the propagation of analyticity of solutions of différential equations with constant coefficients. Arkiv f. Mat. 5 (1964) p. 271-279. | MR | Zbl

[6] Browder F.E.: A remark on the Dirichlet problem for non elliptic self-adjoint partial differential operators. Rend. Cire. Mat. Palermo 6 (1957) p. 249-253. | MR | Zbl

[7] Browder F.E., : On the Dirichlet problem for linear non elliptic partial differential equations. Rend. Circ. Mat. Palermo 7 (1958) p. 303-308. | MR | Zbl

[8] Browder F.E.: Non linear equations of evolutions. Ann. of Math. 80 (1964) p. 485-523. | MR | Zbl

[9] Chaillou J.: Sur les ensembles bornés de diatributions polynomes inversibles et d'inverse borné, et sur les hypersurfaces hyperboliques. Thèse - Paris (1969). | Zbl

[10] Dionne P.: Sur les problèmes de Cauchy hyperboliques bien posés J. An. Math. Jerusalem 10 (1963) p. 1-90. | MR | Zbl

[11] Friedmann A. - Littman W.: Partially characteristic boundary Problems for hyperbolic equations. J. of Math. and Mech. 12 (1963) p. 213-224. | MR | Zbl

[12] Gårding L.: Linear hyperbolic partial differential equations with constant coefficients. Acta Math. 85 (1950) p. 1-62. | MR | Zbl

[13] Gårding L. Solution directs du problème de Cauchy pour les équations hyperboliques. Coll. Inst. C. N. R. S. (1956) p. 71-89. | MR | Zbl

[14] Goulaouic Ch. - Grisvard P.: C. R. Ac. Sc. Paris 268 (1969) p. 1537-1539. | MR | Zbl

[15] Grubb G.: A characterization of the non-local boundary value problems associated with an elliptic operator. Ann. Sc. N. Sup. Pisa 22 (1968) p. 425-513. | Numdam | MR | Zbl

[16] Hadamard J.: Le problème de Dirichlet pour les équations hyperboliques J. Chinese Math. Soc. 2 (1937) p. 6-20. | JFM | Zbl

[17] Hadamard J.: On the Dirichlet problem in the hyperbolic case. Proc. Nat. As. Sc. USA 28 (1942) p. 258-263. | MR | Zbl

[18] Hadamard J.: Sur le cas anormal de l'équation des ondes pour le problème de Cauchy. 1948 - Interscience New-York [repris dans: Oeuvres C. N. R. S. (1968) t. 3 p. 1679-84]. | MR

[19] Hörmander L. Linear Partial Differential Operators, Springer - Berlin - 1963. | MR | Zbl

[20] Hörmander L.: On the theory of general partial differential operators. Acta. Math. 94 (1955) p. 161-248. | MR | Zbl

[21] Kakita T.: Hyperbolic convolution operators. Canad. J. of Math. 17 (1965) p. 559-582. | MR | Zbl

[21bis] Kohn J. - Nirenberg L.: Non coercive boundary problems. Comm. Pure Appl. Math. 18 (1965) p. 443-492. | MR | Zbl

[22] Krée P.: Sur les multiplicateors dans FLP. Ann. Inst. Fourier 16 (1966) p. 31-89. | Numdam | MR | Zbl

[22 bis] Kumano-Go H.: On propagation of regislarity in space variables for the solutions of differeittial equations with constant coefficients. Proc. Jap. Acad. 42 (1966) p. 204-209. | MR | Zbl

[22 ter] Kumano-Go H. - Suinkai K.: The characterization of differential operators with respect to characteristic Cauchy problem. Osaka J. of Math. 3 (1966) p. 155-162. | MR | Zbl

[23] Lax A.: On Cauchy's problem for partial differential equations with multiple characteriatics. Comm. Pure Appl. Math. 9 (1956) p. 135-169. | MR | Zbl

[24] Lax P.D. - Phillips R.S.: Local boundary conditions for dissipative symmetrie linear differential equations. Comm. Pure Appl. Math. 13 (1960) p. 427-455. | MR | Zbl

[25] Leray J.: Hyperbolic differential equations. Princeton (1952). | MR

[26] Lions J.L.: On elliptic partial differential equations. Tata Inst. Bombay (1957).

[27] Lions J.L. - Magenes E.: Problèmes aux limites non-homogènes et applications. 2 vol - Dunod - Paris (1968). | Zbl

[28] Littman W.: The wave operator and LP norms. J. of Math. and Mech. 12 (1963) p. 55-68. | MR | Zbl

[29] Littman W.: Remarks on the Dirichlet problem for general linear partial differential equation. Comm. Pure and Appl. Math. 11 (1958) p. 145-151. | MR | Zbl

[30] Louhivaara I.S.: Über das Dirichletsche Problem für die selbstadjungierten lin. part. Differentialgleiclcungen 2nd Ordnung. Rend. Circ. Mat. Palermo 5 (1956) p. 260-274. | MR | Zbl

[31] Lojasirwicz S.: Sur le problème de division. Studia Mat. 18 (1959) p. 87-136. | MR | Zbl

[32] Morel H.: Introduction de poids dans l'étude de problèmes aux limites Ann. Inst. Fourier 12 (1962) p. 299-414. | Numdam | MR | Zbl

[33] Pevser G.: Energy inequalities for hyperbolic equations in seneral variables with multiple characteristic and constant coefficients. Trans. A. M. S. 108 (1963) p. 478-490. | MR | Zbl

[34] Phillips R.S.: Dissipative operators and hyperbolic systems of partial differential equations. Trans. A. M. S. 90 (1959) p. 193-254. | MR | Zbl

[35] Piiillips R.S.: Semi-groups of contraction operators. Cours CIME-Varenna. | Zbl

[36] Schechter M.: Negative norms and boundary problems. Ann. of Math. 72 (1960) p. 581-593. | MR | Zbl

[37] Schechter M.: Some unusual boundary value problems Proc. of 4th symp. in pure Math. A. M. S. Berkeley (1960). | MR | Zbl

[38] Schwartz L.: Théorie des Distributions. Hermann, Paris (1967). | MR | Zbl

[39] Schwirtz L.: Sous espaces hilbertiens d'espaces vectoriels topologiques et noyaux associés. J. Ann. Math. Jérnealem 13 (1964) p. 115-256. | MR | Zbl

[39bis] Shinkai K.:A note on regularity of null solutions. Proc. Jap. Acad. 43 (1967) p. 134-137. | MR | Zbl

[40] Strichartz R.: Sobolev inequalities and extension theorems for functions with certain Lp derivatives. Sémin. Orsay (1967) multigraphié.

[41] Talenti G.: Una diseguaglianza integrale. Boll. U. M. I. 21 (1966) p. 25-34. | MR | Zbl

[42] Talfnti G.: Sopra una diseguaglianza integrale. Ann. Sc. Norm. Sup. Pisa 21 (1967) p. 167-188. | Numdam | MR | Zbl

[43] Trèves F.: Relations de domination entre opérateurs différentiels. Acta Math. 101 (1959) p. 1-139. | MR | Zbl

[44] Trêves F. - Zerner M.: Zones d'analyticité des solutions élémentaires, Bull S. M. F. 95 (1967) p. 155-192. | Numdam | MR | Zbl

[45] Yosida K.: Functional analysis. Springer, Berlin (1965).

[46] Zerner M.: Solutions singulieres d'équations aux dérivéea partielles. Bull. S. M. F. 91 (1963) p. 203-226. | Numdam | MR | Zbl