Propriétés et existence des solutions de certaines classes d'équations du type elliptique
Bulletin de la Société Mathématique de France, Tome 86 (1958), pp. 283-297.
@article{BSMF_1958__86__283_0,
     author = {Gillis, Paul P.},
     title = {Propri\'et\'es et existence des solutions de certaines classes d'\'equations du type elliptique},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {283--297},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {86},
     year = {1958},
     doi = {10.24033/bsmf.1507},
     mrnumber = {21 #3659},
     zbl = {0087.30104},
     language = {fr},
     url = {http://www.numdam.org/articles/10.24033/bsmf.1507/}
}
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Gillis, Paul P. Propriétés et existence des solutions de certaines classes d'équations du type elliptique. Bulletin de la Société Mathématique de France, Tome 86 (1958), pp. 283-297. doi : 10.24033/bsmf.1507. http://www.numdam.org/articles/10.24033/bsmf.1507/

[1]Agmon (S.). - Multiple layer potentials and the Dirichlet problem for higher order elliptic equations in the plane (Comm. pure appl. Math., vol. 10, 1957, p. 179-239). | MR | Zbl

[2]Aronsajn (N.). - On coercive integro-differential forms (Studies in Eigenvalue Problems, no 14, Lawrence Kansas, 1955, p. 94-106). | Zbl

[3]Aronsajn (N.). - A unique continuation theorem for all partial differential equations and inequalities of second order (Bull. Amer. math. Soc., vol. 62, Abstract 184, 1956, p. 154).

[4]Bers (L.). - Survey of local properties of solutions of elliptic partial differential equations (Comm. pure appl. Math., vol. 9, 1956, p. 339-350). | MR | Zbl

[5]Bers (L.) et Nirenberg (L.). - Boundary value problems for nonlinear elliptic equations in two independent variables (Proc. Int. Congress Amsterdam, 1954, p. 84-85).

[6]Bers (L.) et Nirenberg (L.). - On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications (Convegno internazionale sulle equazioni derivate e parziali, 1954, p. 111-140). | MR | Zbl

[7]Bers (L.) et Nirenberg (L.). - On linear and nonlinear elliptic boundary value problems in the plane (Convegno internationale sulle equazioni derivate e parziali, 1954, p. 141-167). | MR | Zbl

[8]Browder (F. E.). - The Dirichlet problem for linear elliptic equations of arbitrary even order with variable coefficients (Proc. nat. Acad. Sc. U.S.A., vol. 38, no 3, 1952, p. 230-235). | MR | Zbl

[9]Browder (F. E.). - The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order (Proc. nat. Acad. Sc. U.S.A., vol. 38, no 8, 1952, p. 741-747). | MR | Zbl

[10]Browder (F. E.). - Assumption of boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation (Proc. nat. Acad. Sc. U.S.A., vol. 39, no 3, 1953, p. 179-184). | MR | Zbl

[11]Browder (F. E.). - Linear parabolic differential equations of arbitrary order ; general boundary-value problems for elliptic equations (Proc. nat. Acad. Sc. U.S.A., vol. 39, no 3, 1953, p. 185-190). | MR | Zbl

[12]Browder (F. E.). - Strongly elliptic systems of differential equations (Contributions to the Theory of partial differental equations, Ann. Math. Studies no 33, Princeton, 1954, p. 15-51). | MR | Zbl

[13]Browder (F. E.). - Regularity properties of solutions of elliptic differential equations (Abstract 695, Bull. Amer. math. Soc., vol. 61, 1955, p. 528).

[14]Browder (F. E.). - On the regularity properties of solutions of elliptic differential equations (Comm. pure appl. Math., vol. 9, 1956, p. 351-361). | MR | Zbl

[15]Calderon (A. P.) et Zygmund (A.). - On the existence of singular integrals (Acta Math., vol. 88, 1952, p. 85-139). | MR | Zbl

[16]Carleman (T). - Sur les systèmes linéaires aux dérivées partielles du premier ordre à deux variables (C. R. Acad. Sc. Paris, t. 197, 1933, p. 471-474). | JFM | Zbl

[17]Carleman (T.). - Sur un problème d'unicité pour les systèmes d'équations aux dérivées partielles à deux variables indépendantes (Ark. Mat. Astr. Fys., vol. 26 B, no 17, 1939, p. 1-9). | JFM | MR | Zbl

[18]Cordes (H. O). - Über die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen (Math. Ann., vol. 131, 1956, p. 278-312). | EuDML | MR | Zbl

[19]Courant (R.) et Hilbert (D.). - Methoden der mathematischen Physik, vol. 2, chap. 7, Berlin, Springer, 1937. | EuDML | JFM | Zbl

[20]De Giorgi (E.). - Un esempio di non-unicità della soluzione del problema di Cauchy, relativo ad una equazione differenziale lineare a derivate parziali di tipo parabolico (Rend. Mat. e Appl., 5e série, vol. 14, 1955, p. 382-387). | MR | Zbl

[21]Douglis (A.). - Uniqueness in Cauchy problems for elliptic systems of equations (Comm. pure appl. Math., vol. 6, 1953, p. 291-298). | MR | Zbl

[22]Douglis (A.) et Nirenberg (L.). - Interior estimates for elliptic systems of partial differential equations (Comm. pure appl. Math., vol. 8, 1955, p. 503-538). | MR | Zbl

[23]Friedrichs (K. O.). - On differential operators in Hilbert spaces (Amer. J. Math., vol. 61, 1939, p. 523-544). | JFM | Zbl

[24]Kriedrichs (K. O.). - The identity of weak and strong extensions of differential operators (Trans. Amer. math. Soc., vol. 55, no 1, 1944, p. 132-151). | MR | Zbl

[25]Friedrichs (K. O.). - Differentiability of solutions of elliptic differential equations (Comm. pure appl. Math., vol. 6, 1953, p. 299-326). | MR | Zbl

[26]Gårding (L.). - Le problème de Dirichlet pour les équations aux dérivées partielles elliptiques homogènes à coefficients constants (C. R. Acad., Sc. Paris, t. 230, 1950, p. 1030-1032). | MR | Zbl

[27]Gårding (L.). - Dirichlet's problem for linear elliptic partial differential equations (Math. Scand., vol. 1, 1953, p. 55-72). | EuDML | MR | Zbl

[28]Gillis (P. P.). - Sur certaines classes d'équations aux dérivées-partielles (Acad. Roy. Belgique, Bull. Cl. Sc., vol. 22, 1936, p. 835-854 et 941-947). | JFM | Zbl

[29]Gillis (P. P.). - Sur les problèmes réguliers du calcul des variations (Studia Mathematica, vol. 8, 1938, p. 68-77). | EuDML | JFM | Zbl

[30]Gillis (P. P.). - Équations de Monge-Ampère à quatre variables indépendantes (Acad. Roy. Belgique, Bull. Cl. Sc., vol. 36, 1950, p. 474-484). | MR | Zbl

[31]Gillis (P. P.). - Équations de Monge-Ampère à six variables indépendantes (Acad. Roy. Belgique, Bull. Cl. Sc., vol. 37, 1951, p. 229-240). | MR | Zbl

[32]Guseva (O. V.). - On boundary problems for strongly elliptic systems (Doklady Akad. Nauk S. S. S. R., vol. 12, 1955, p. 1069-1072). | MR | Zbl

[33]Haar (A.), - Zur Variationsrechnung (Abh. Math. Sem. Hamburgischen Univ. vol. 8, 1930, p. 1-27). | JFM

[34]Hartman (P) et Wintner (A.). - On the local behavior of solutions of non-parabolic partial differential equations (Amer. J. Math., vol. 75, 1953, p. 449-476). | MR | Zbl

[35]Hartman (P.) et Wintner (A.). - On the tocal behavior of solutions of non-parabolic partial differential equations. III : Approximations by spherical means (Amer. J. Math., vol. 77, 1955, p. 453-483). | MR | Zbl

[36]Heinz (E.). - Über die Eindeutigkeit beim Cauchyschen Anfangswertproblem einer elliptischen Differentialgleichung zweiter Ordnung (Nachr. Akad. Wiss. Göttingen, Math. Phys., Kl. II a, n° 1, 1955, p. 1-12). | MR | Zbl

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

[38]John (F.). - On linear partial differential equations with analytic coefficients (Comm. pure appl. Math., vol. 2, 1949, p. 209-253). | MR | Zbl

[39]John (F.). - The fundamental solution of linear elliptic differential equations with analytic coefficients (Comm. pure appl. Math., vol. 3, 1950, p. 273-304). | MR | Zbl

[40]John (F.). - Derivatives of continuous weak solutions of linear elliptic equations (Comm. pure appl. Math., vol. 6, 1953, p. 327-335). | MR | Zbl

[41]John (F.). - Plane waves and spherical means applied to partial differential equations, New-York, Interscience Publ., 1955. | MR | Zbl

[42]Lax (P. D.). - On Cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations (Comm. pure appl. Math., vol. 8, 1955, p. 615-633). | MR | Zbl

[43]Lax (P. D.). - A stability theorem for solutions of abstract differential equations and its application to the study of the local behavior of solutions of elliptic equations (Comm. pure appl. Math., vol. 9, 1956, p. 747-766). | MR | Zbl

[44]Leray (J.) et Schauder (J.). - Topologie et équations fonctionnelles (Ann. scient. Éc. Norm. Sup., t. 51, 1934, p. 45-78). | EuDML | JFM | Numdam | Zbl

[45]Lions (J. L.). - Sur les problèmes de dérivées obliques (C. R. Acad. Sc. Paris, t. 240, 1955, p. 266-268). | MR | Zbl

[46]Lions (J. L.). - Problèmes aux limites en théorie des distributions (Acta Math., vol. 94, 1955, p. 13-153). | MR | Zbl

[47]Lopatinskii (Ya. B.). - On a method of reducing boundary problems for a system of differential equations of elliptic type to regular equations (Ukrain. Mat. Ž., t. 5, 1953, p. 123-151). | MR

[48]Malgrange (B.). - Exixtence et approximation des solutions des équations aux dérivées partielles et des équations de convolution (Thèse Sc. math., Paris, 1955).

[49]Milgram (A.) et Rosenbloom (P. C.). - Harmonic forms and heat conduction. | Zbl

Milgram (A.) et Rosenbloom (P. C.) I : Closed Riemannian manifols ;

Milgram (A.) et Rosenbloom (P. C.) II : Heat distribution on complexes and approximation theory (Proc. Nat. Acad. Sc. U. S. A., vol. 37, 1951, p. 180-184 et 435-438). | MR | Zbl

[50]Miranda (C). - Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche di due variabili (Giorn. Mat. Battaglini, vol. 78, 1948-1949, p. 97-118). | MR | Zbl

[51]Miranda (C.). - Sui sisteme di tipo ellittico di equazioni lineari a derivate parziali del primo ordine, in n variabili indipendenti (Atti delle Ac. naz. dei Lincei., 8e série, 1 a, vol. 3, 1952, p. 85-121). | MR | Zbl

[52]Miranda (C.). - Equazioni alle derivate parziali di tipo ellitico, Berlin, Springer, 1955. | Zbl

[53] Morrey (C. B.). - Multiple integral problems in the calculus of variations and related topics (Univ. Calif. Publ. Math., nouv. série, vol. 1, 1943, p. 1-130). | MR | Zbl

[54] Morrey (C. B.). - Second order elliptic systems of differential equations (Contribution to the theory of partial differential equations, Ann. math. Studies n° 33, Princeton, 1954, p. 101-159). | MR | Zbl

[55] Morrey (C. B.). - A variational method in the theory of harmonic integrals, II (Amer. J. Math., vol. 78, 1956, p. 137-170). | MR | Zbl

[56] Morrey (C. B.) et Eells (J.). - A variational method in the theory of harmonic integrals, I (Ann. of Math., vol. 63, 1956, p. 91-128). | MR | Zbl

[57] Morrey (C. B.) et Nirenberg (L.). - On the analyticity of the solutions of linear elliptic systems of partial differential equations (Comm. pure appl. Math., vol. 10, 1957, p. 271-290). | MR | Zbl

[58] Müller (C). - On the behavior of solutions of the differential equation Δu = F(x, u) in the neighbourhood of a point (Comm. pure appl. Math., vol. 7, 1954, p. 505-515). | Zbl

[59] Nash (J). - Parabolic equations (Proc. nat. Acad. Sc. U.S.A., vol. 43, 1957, p. 754-758). | MR | Zbl

[60] Nirenberg (L.). - On nonlinear elliptic partial differential equation and Hölder continuity (Comm. pure appl. Math., vol. 6, 1953, p. 103-156). | MR | Zbl

[61] Nirenberg (L.). - On a generalization of quasi-conformal mappings and its application to elliptic partial differential equations (Contribution to the theory of partial differential equations, Ann. math. studies, n° 33, Princeton, 1954, p. 95-100). | MR | Zbl

[62] Nirenberg (L). - Remarks on strongly elliptic partial differential equations (Comm. pure appl. Math., vol. 8, 1955, p. 649-676). | MR | Zbl

[63] Nirenberg (L.). - Estimates and existence of solutions of elliptic equations (Comm. pure appl. Math., vol. 9, 1956, p. 509-552). | MR | Zbl

[64] Nirenberg (L.). - Uniqueness in Cauchy problems for differential equations with constant leading coefficients (Comm. pure appl. Math., vol. 10, 1957, p. 89-105). | MR | Zbl

[65] Pleijel (A.). - On Green's functions for elastic plates with clamped, supported and free edges (Proc. Symposium on spectral theory and differential problems, Oklahoma, 1951, p. 413-437). | MR | Zbl

[66] Plis (A.). - The problem of uniqueness for the solution of a system of partial differential equations (Bull. Acad. polon. Sc., Cl. III, 2, 1954, p. 55-57). | MR | Zbl

[67] Rado (T.). - Über zweidimensionale reguläre Variationsprobleme ... (Math. Ann., vol. 101, 1929, p. 620-632). | EuDML | JFM

[68] Schauder (J.). - Über lineare elliptische Differentialgleichungen zweiter Ordnung (Math. Z., vol. 38, 1934, p. 257-282). | EuDML | JFM | Zbl

[69] Schauder (J.). - Numerische Abschätzungen in elliptischen linearen Differentialgleichungen (Stud. Math., vol. 5, 1934, p. 34-42). | EuDML | JFM | Zbl

[70] Schwartz (L.). - Théorie des distributions, Paris, Hermann, 1950-1951. | Zbl

[71] Sobolev (S. L.). - On a theorem of functional analysis (Mat. Sbornik, nouv. série, vol. 4, 1938, p. 471-497). | JFM | Zbl

[72] Van Hove (L.). - Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieurs fonctions inconnues (Indag. Math., vol. 7, n° 1, 1947, p. 3-8). | MR | Zbl

[73] Van Hove (L.). - Sur le signe de la variation seconde des intégrales multiples à plusieurs fonctions inconnues (Acad. Roy. Belgique, Cl. Sc., Mémoires, vol. 24, fasc. 5, p. 1-68). | MR | Zbl

[74] Vekua (N). - On a method of solving boundary value problems for partial differential equations (Doklady Akad. Nauk. S. S. S. R., vol. 101, 1955, p. 593-596). | Zbl

[75] Vishik (M. I.). - The method of orthogonal and direct decomposition in the theory of elliptic differential equations (Math. Sbornik, nouv. série, vol. 25, 1949, p. 189-234). | MR | Zbl

[76] Vishik (M. I.). - On strongly elliptic systems of differential equations (Mat. Sbornik, nouv. série, vol. 29, 1951, p. 615-676). | MR | Zbl

[77] Vishik (M. I.). - On general boundary problems for elliptic differential equations (Trudy Moskov. Mat. Obsč., vol. 1, 1952, p. 187-246). | MR | Zbl

[78] Von Neumann (J.). - Über einen Hilfssatz der Variationsrechnung (Abh. Mat. Sem. Hamburgischen Univ., vol. 8, 1930, p. 28-31). | JFM

[79] Weyl (H.). - The method of orthogonal projection in potential theory (Duke Math. J., vol. 7, 1940, p. 411-444). | JFM | MR | Zbl

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