×

Functional analysis and partial differential equations. II. (English) Zbl 0103.31602


PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] Agmon, S., A. Douglis andL. Nirenberg: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Communs Pure App. Math.12, 623-727 (1959). · Zbl 0093.10401
[2] Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. math. pures app.36, 235-249 (1957). · Zbl 0084.30402
[3] Banach, S.: Théorie des Opérations Lineaires. Warsaw 1932.
[4] Beckert, H.: Eine bemerkenswerte Eigenschaft der Lösungen des Dirichletschen Problems bei linearen elliptischen Differentialgleichungen. Math. Ann.139, 255-264 (1959). · Zbl 0095.30402
[5] Birman, M.: On the theory of general boundary problems for elliptic differential equations. Dokladi Akad. Nauk SSSR (N. S.)92, 205-208 (1953).
[6] Browder, F. E.: The Dirichlet problem for linear elliptic equations of arbitrary even order with variable coefficients. Proc. Nat. Acad. Sci.38, 230-235 (1952). · Zbl 0046.32302
[7] Browder, F. E.: On the eigenfunctions and eigenvalues of the general linear differential operator. Proc. Nat. Acad. Sci.39, 433-439 (1953). · Zbl 0050.32102
[8] Browder, F. E.: Strongly elliptic systems of differential equations. Ann. Math. Study No.33, 15-51 (1954). · Zbl 0057.32901
[9] Browder, F. E.: On the regularity properties of solutions of elliptic differential equations. Communs Pure App. Math.9, 351-361 (1956). · Zbl 0070.09601
[10] Browder, F. E.: Parabolic systems of differential equations with time-dependent coefficients. Proc. Nat. Acad. Sci.42, 914-917 (1956). · Zbl 0074.07903
[11] Browder, F. E.: Regularity theorems for solutions of partial differential equations with variable coefficients. Proc. Nat. Acad. Sci.43, 234-236 (1957). · Zbl 0079.11601
[12] Browder, F. E.: La théorie spectrale des opérateurs aux dériveés partielles du type elliptique. C. R. Acad. Sci. (Paris)246, 536-528 (1958). · Zbl 0088.30503
[13] Browder, F. E.: Eigenfunction expansions for non-symmetric partial differential operators. III. Am. J. Math.81, 715-734 (1959). · Zbl 0103.31701
[14] Browder, F. E.: On functional analysis and partial differential equations. I. Math. Ann.138, 55-79 (1959). · Zbl 0086.10301
[15] Browder, F. E.: Estimates and existence theorems for elliptic boundary value problems. Proc. Nat. Acad. Sci.45, 365-372 (1959). · Zbl 0093.29402
[16] Browder, F. E.: On the spectral theory of elliptic differential operators. I. Math. Ann.142, 22-130 (1961). · Zbl 0104.07502
[17] Browder, F. E.: A priori estimates for solutions of elliptic boundary value problems. I and II. Proc. Koninkl. Ned. Akad. Wetenschap.22, 145-159, 160-169 (1960). · Zbl 0096.30202
[18] Browder, F. E.: A continuity property for adjoints of closed operators in Banach spaces and its applications to elliptic boundary value problems, Duke Math. J.28, 157-182 (1961). · Zbl 0102.31502
[19] Calderon, A. P.: Uniqueness in the Cauchy problem for partial differential equations, Am. J. Math.80, 16-36 (1958). · Zbl 0080.30302
[20] Calderon, A. P., andA. Zygmund: On the existence of certain singular integrals. Acta Math.88, 85-139 (1952). · Zbl 0047.10201
[21] Calderon, A. P., andA. Zygmund: On singular integrals. Am. J. Math.78, 289-309 (1956). · Zbl 0072.11501
[22] Carleman, T.: Sur un problème d’unicité pour les systèmes d’équations aux dérivées partielles à deux variables independents. Arkiv Mat.26 B, No. 17, 1-9 (1939). · Zbl 0022.34201
[23] Cordes, H. O.: Über die Bestimmtheit der Lösungen elliptischer Differentialgleichungen durch Anfangsvorgaben. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa, No.11, 239-258 (1956). · Zbl 0074.08002
[24] Dieudonné, J. andL. Schwartz: La dualité dans les espaces (?) et (? ?. Ann. Inst. Fourier1, 61-101 (1949). · Zbl 0035.35501
[25] Douglis, A., andL. Nirenberg: Interior estimates for elliptic systems of partial differential equations. Communs Pure App. Math.8, 503-538 (1955). · Zbl 0066.08002
[26] Dunford, N., andJ. T. Schwartz: Linear Operators Vol. I. New York 1958.
[27] Eidelman, S.: Estimates for solutions of parabolic equations and some of their applications. Mat. Sbornik33, 359-382 (1953). · Zbl 0052.10003
[28] Friedrichs, K. O.: On the differentiability of solutions of linear elliptic differential equations. Communs Pure App. Math.6, 299-326 (1953). · Zbl 0051.32703
[29] Gelfand, I. N., andG. E. Silov: Generalized Functions, 3 vols. Moscow 1958.
[30] Giraud, G.: Sur les équations du type elliptique et la méthode des approximations successives. J. math. pures appl.8, 269-300 (1929). · JFM 55.0285.01
[31] Gohberg, I. C., andN. G. Krein: The basic propositions on defect numbers, root numbers, and indices of linear operators. Uspekhi Mat. Nauk (N. S.)12, 43-118 (1957) (Am. Math. Soc. Translations, Series 2, vol.13.)
[32] Greco, D.: Nuovo formale integrali di maggiorazione per le soluzioni di un’equazione lineare di tipo ellittico e applicazioni alla teoria del potenziale. Ricerche Mat.5, 126-149 (1956). · Zbl 0072.31001
[33] Grothendieck, A.: Sur les espaces de solutions d’une classe générale d’équations aux dérivées partielles. J. Anal. Math.2, 243-280 (1953). · Zbl 0051.08801
[34] Grothendieck, A.: Espaces Vectoriels Topologiques. Sao Paulo 1954. · Zbl 0058.33401
[35] Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Mem. Am. Math. Soc. No. 16, 1955. · Zbl 0123.30301
[36] Hadamard, J.: Lectures on Cauchy’s Problem. New Haven 1923. · JFM 49.0725.04
[37] Hartman, P., andA. Wintner: On the local behavior of solutions of non-parabolic partial differential equations. III. Am. J. Math.77, 453-483 (1955). · Zbl 0066.08001
[38] Heinz, E.: Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung Zweiter Ordnung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa, No. 1, 1-12 (1955). · Zbl 0067.07503
[39] Hopf, E.: Zum analytischen Charakter der Lösungen regulärer zweidimensionaler Variationsprobleme. Math. Z.30, 404-413 (1929). · JFM 55.0898.03
[40] Hopf, E.: Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen Zweiter Ordnung. Math. Z.34, 191-233 (1931). · Zbl 0002.34003
[41] Hörmander, L.: On the theory of general partial differential operators. Acta Math.94, 161-248 (1955). · Zbl 0067.32201
[42] Hörmander, L.: On the interior regularity of the solutions of partial differential equations. Communs Pure App. Math.11, 197-218 (1958). · Zbl 0081.31501
[43] Hörmander, L.: Definitions of maximal differential operators. Arkiv Mat.3, 501-504 (1958). · Zbl 0131.09403
[44] Hörmander, L.: On the uniqueness of the Cauchy problem II. Math. Scand.7, 177-190 (1959). · Zbl 0090.08001
[45] John, F.: General properties of solutions of linear elliptic partial differential equations. Proc. Symposium on Spectral Theory and Differential Problems, Stillwater, Oklahoma 1951.
[46] Joichi, J. T.: On closed operators with closed range. Proc. Am. Math. Soc.11, 80-83 (1960). · Zbl 0090.09101
[47] Kato, T.: Perturbation theory for nullity, deficiency and other quantities of linear operators. J. d’Analyse Math.6, 261-322 (1958). · Zbl 0090.09003
[48] Keldych, M. V.: On the eigenvalues and eigenfunctions of certain classes of non self-adjoint equations. Dokladi Akad. Nauk SSSR (N. S.)77, 11-14 (1951).
[49] Koshelev, A. I.: On a priori estimates inL p of generalized solutions of elliptic equations and systems. Uspekhi Mat. Nauk13, 29-88 (1958).
[50] Landis, E. M.: Some questions of the qualitative theory of elliptic and parabolic equations. Uspekhi Mat. Nauk14, 21-85 (1959).
[51] Lax, P. D.: A stability theory of abstract differential equations and its application to the study of local behaviour of solutions of elliptic equations. Communs Pure App. Math.8, 747-766 (1956). · Zbl 0072.33004
[52] Lichtenstein, N.: Über den analytischen Charakter der Lösungen zwei-dimensionaler Variationsprobleme. Bull. Acad. Sci. Cracouv. Ser. A (1912), pp. 915-941. · JFM 43.0470.01
[53] Lions, J. L.: Lectures on elliptic partial differential equations. Tata Institute Lecture Notes. Bombay 1957.
[54] Lopatinski, Ya. B.: Fundamental solution of a system of differential equations of elliptic type. Ukranian Mat. J.1, 42-63 (1949).
[55] Lubich, U. I.: On the fundamental solution of linear partial differential equations of elliptic type. Mat. Sbornik39, 23-38 (1956).
[56] Malgrange, B.: Existence et approximation des solutions des équations aux derivées partielles et des équations de convolution. Ann. Inst. Fourier6, 271-355 (1956). · Zbl 0071.09002
[57] Malgrange, B.: Sur une classe d’opérateurs differentiels hypoelliptiques. Bull. soc. math. France85, 283-306 (1957). · Zbl 0082.09303
[58] Mergelyan, S. N.: Uniform approximations to functions of a complex variable. Uspekhi Mat. Nauk (N. S.)7, 31-122 (1952). (A. M. S. Trans. Ser. 1, No. 101.) · Zbl 0059.05902
[59] Miranda, C.: Equazioni alle derivate parziali di tipo ellitico. Ergeb. Math. N. S.2, 1955. · Zbl 0065.08503
[60] Mizohata, S.: Hypoellipticité des équations paraboliques. Bull. soc. math. France85, 15-56 (1957).
[61] Mizohata, S.: Unicité du prolongement des solutions des équations elliptiques du quatrième ordre. Proc. Jap. Acad.34, 687-692 (1958). · Zbl 0085.08501
[62] Mizohata, S., andY. Homada: Hypoellipticité. Proc. Jap. Acad.34, 482-486 (1958). · Zbl 0093.29304
[63] Morrey, C. B., jr.: On the analyticity of the solutions of analytic non-linear elliptic systems of partial differential equations. I. Am. J. Math.80, 198-218 (1958). · Zbl 0081.09402
[64] Müller, C.: On the behaviour of the solutions of the differential equation ?u=F (x, u) in the neighborhood of a point. Comment. pure app. Math.7, 505-515 (1954). · Zbl 0056.32201
[65] Neumark, M. A.: Spectral analysis of non-self adjoint operators. Uspekhi Mat. Nauk11, 183-202 (1956). · Zbl 0073.09802
[66] Nirenberg, L.: Remarks on strongly elliptic partial differential equations. Communs Pure App. Math.8, 649-675 (1955). · Zbl 0067.07602
[67] Nirenberg, L.: Estimates and existence of solutions of elliptic equations. Communs Pure App. Math.9, 509-530 (1956). · Zbl 0070.32301
[68] Peetre, J.: Théorèmes de régularité pour quelques classes d’opérateurs différentiels. Thesis, Lund., Nov. 1959.
[69] Petrovsky, I. G.: Sur l’analyticité des solutions des systèmes d’équations différentielles. Mat. Sbornik.5, 3-70 (1939).
[70] Plis, A.: Non-uniqueness in Cauchy’s problem for differential equations of elliptic type. J. Math. and Mech.9, 557-562 (1960). · Zbl 0093.29303
[71] Rota, G. C.: Extension theory of differential operators. I. Communs Pure App. Math.11, 23-65 (1958). · Zbl 0088.06303
[72] Schauder, J.: Über lineare elliptische Differentialgleichungen zweiter Ordnung. Math. Z.38, 257-282 (1934). · Zbl 0008.25502
[73] Schwartz, L.: Théorie des distributions. Paris 1951. · Zbl 0042.11405
[74] Trèves, F.: Opérateurs différentiels hypoelliptiques. Ann. Inst. Fourier9, 1-73 (1959). · Zbl 0197.36602
[75] Visik, M. I.: On general boundary problems for elliptic differential equations. Trudi Moscow Mat. Soc.1, 187-246 (1952).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.