@article{ASNSP_1960_3_14_1_1_0, author = {Morrey, Charles B. Jr}, title = {Multiple integral problems in the calculus of variations and related topics}, journal = {Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche}, pages = {1--61}, publisher = {Scuola normale superiore}, volume = {Ser. 3, 14}, number = {1}, year = {1960}, mrnumber = {115117}, zbl = {0094.08104}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1960_3_14_1_1_0/} }
TY - JOUR AU - Morrey, Charles B. Jr TI - Multiple integral problems in the calculus of variations and related topics JO - Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche PY - 1960 SP - 1 EP - 61 VL - 14 IS - 1 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1960_3_14_1_1_0/ LA - en ID - ASNSP_1960_3_14_1_1_0 ER -
%0 Journal Article %A Morrey, Charles B. Jr %T Multiple integral problems in the calculus of variations and related topics %J Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche %D 1960 %P 1-61 %V 14 %N 1 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1960_3_14_1_1_0/ %G en %F ASNSP_1960_3_14_1_1_0
Morrey, Charles B. Jr. Multiple integral problems in the calculus of variations and related topics. Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 14 (1960) no. 1, pp. 1-61. http://archive.numdam.org/item/ASNSP_1960_3_14_1_1_0/
[1] Functional spaces and functional completion, Ann. Inst. Fourier Grenoble 6 (1956), 125-185. | Numdam | MR | Zbl
and ,[2] Strongly elliptic systems of differential equations, Contributions to the theory of partial differential equations, 15-51. Ann. of Math. Studies, No 33.Princeton University Press (1954). | MR | Zbl
,[3] - , Numerous notes in Proc, Nat. Acad. Sci. U.S.A. 38 (1952), 230-235 and 741-747; 39 (1953), 179-184 and 185-190; and many others.
[4] Functions of several variables and ab80lute continuity, I, Duke Math. J. 6 (1940), 170-185. | JFM | MR | Zbl
,[5] An éxistence theorem of the calculics of variations for integrals on parametric surfaces, Amer. J. Math. 74 (1952); 265-295. | MR | Zbl
,[6] Sopra l'estremo assoluto degli integrali doppi in forma ordinaria, Ann. Math. Pura Appl, (4) 30 (1949) 249-260. | MR | Zbl
,[7] Plateau's problem and Dirichlet's principle, Ann. of Math. (2) 38 (1937) 679-724. | JFM | MR | Zbl
,[8] - , Dirichlet's principle, conformal mapping, and minimal surfaces, Interscience Press, New York (1950).
[9] On the existence of minimizing surfaces in parametric double integral problems in the calculus of variations, Rev. Math. Univ. Parma 3 (1952) 43-63. | MR | Zbl
,[10] Sull'analiticità delle extremali degli integrali multipli, Atti Accad. Naz. dei Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 20 (1956), 438-441. | MR | Zbl
,[11] Les potentiels d'energie fini Acta Math. 82 (1950), 107-183. | MR | Zbl
,[12] Harmonic Integrals (mimeographed notes), Institute for Advanced Study, Princeton, N. J. (1950). | MR
and ,[13] Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. 56 (1952), 128-156. | MR | Zbl
and ,[14] Fundamental points of potential theory, Rice Inst. Pamphlets 7 (1920), 252-359. | JFM
,[15] - , Note on a theorem of Bôcher, Amer. J. Math. 50 (1928), 123-126. | JFM | MR
[16] - , Potentials of positive mass I. Trans. Amer. Math. Soc. 37 (1935), 226-253. | JFM | MR
[17] Esistenza del minimo in un ctassico problema en calcul delle variazioni, Atti Accad. Naz. Lincei Rend. Cl. Soi. Fis. Mat. Naz. (8) 11 (1951), 34-39. | MR | Zbl
,[18] On the identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55 (1944), 132-151. | MR | Zbl
,[19] - , On the differentiability of the solutions of linear elliptic differential equations, Comm. Pure Appl. Math. 6 (1953), 299-326. | MR | Zbl
[20] - , On differential forms on Riemannian manifolds, Comm. Pure Appl. Math. 8 (1955), 551-558. | MR | Zbl
[21] Il principio di minimo e i teoremi di esistenza per i problemi di contorno relativi alle equazioni alle derivate parziali di ordine pari, Rend. Circ. Mat. Palermo 23 (1907), 58-84.
,[22] The harmonic operator for exterior differential forms, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 48-50. | MR | Zbl
,[23] - , The heat equation method of Milgram and Roeenbloom for open Riemanniam manifolds, Ann. Of Math. 60 (1954), 458-466. | MR | Zbl
[24] Dirichlet's problem for linear elliptic partial differential equations, Math. Scad. 1 (1953), 55-72. | Zbl
,[25] A Dirichlet problem for harmonic functionals with applications to analytic varieties, Proc. London Math. Soc. (2) 36 (1935), 257-303. | JFM | Zbl
,[26] - , The Theory and Applications of Harmonic Integrals, Second Edition, Cambridge University Press 1952. | MR | Zbl
[27] Zum analytischen Charakter der Lösungen regulärer zweidimensionaler Variationsprobleme, Math. Zeit. 30 (1929), 404-413. | JFM | MR
,[28] Derivatives of continuous weak solutious of linear elliptic equations, Comm. Pure Appl. Math. 6 (1953) 327-335. | MR | Zbl
,[29] Harmonic fields in Riemannian manifolda, Ann. of Math. 50 (1949), 587-665. | MR | Zbl
,[30] On Cauchy's problem for hyperboLic equations and the differentiability of the solutions of elliptic equations, Comm. Pure Appl. Math. 8 (1955), 615-633. | MR | Zbl
,[31] Sur Le problème de Dirichlet, Rend. Circ. Mat. Palermo 24 (1907), 371-402. | JFM
,[32] Sul principio di Dirichlet, Rend. Ciro. Mat. Palermo 22 (1906). 293-359. | JFM
,[33] On minimal surfaoes with partially free boundary, Comm. Pure Appl. Math. 4 (1952), 1-13.
,[34] Uber den analytischen Charakter der Lösungen zweidimensionaler Variatiosprobleme, Bull. Acad. Sci. Cracovia, Cl. Sci. Mat. Nat. (A) (1912), 915-941. | JFM
,[35] - , Zur Theorie der Konforme Abbildutig. Konforme Abbildung nichtanalyticher singularitatenfreier FLachenstiiche auf ebene Gebiete, Bull. Int. Acad. Sci. Cracovia, Mat. Nat. Cl. (A) (1916), 192-217.
[36] Integrals ovsr surfaces in parametric form, Ann. of Math. 34 (1933), 815-838. | JFM | MR | Zbl
,[37] - , Parametrizations of saddle surfaces with application to the problem of Plateau, Trans. Amer. Math. Soc. 35 (1934), 718-733. | JFM | Zbl
[38] Harmoníc forms and heat conduction, Proc. Nat. Acad. Soi. U.S.A. 37 (1951), 180-184 and 435-438. | Zbl
and ,[39] On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soo. 43 (1938), 126-166. | JFM | MR | Zbl
, Jr.[40] - , Functiona of several variables and absolute continuity II, Duke Math. J. 6 (1940), 187-215. | JFM | MR | Zbl
[41] - , A eorrection to a previous paper, Duke Math. J. 9 (1942), 120-124. | MR | Zbl
[42] - Multiple integral problems in the calculus of variations and related topica, Univ. of Calif. Publications in Math. new ser. 1 (1943), 1-130. | MR | Zbl
[43] - , The problem of Plateau on a Riemannian manifold, Ann. of Math. 49 (1948), 807-851. | MR | Zbl
[44] - , Quasi-convexity and the lower-semicontinuity of multiple integrate, Pac. J. Math. 2 (1952), 25-53. | MR | Zbl
[45] - , Seoond order elliptic systems of differential equations, Ann. of Math. Studies No. 33 Princeton University Press, 1954, 101-159. | MR | Zbl
[46] - , A variatioval method in the theory of harmonic integrals, II Amer. J. Math. 78 (1956), 137-170. | MR | Zbl
[47] A variational method in the theory of harmonic integrals I, Ann. of Math. 63 (1956), 91-128. | MR | Zbl
and ,[48] Uber die gleichmässige Sumierbarkeit und ihre Anwendung auf ein Variationsproblem, Jap. J. Math. 6 (1929), 173-182. | JFM
,[49] Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954. | MR | Zbl
,[50] Sur une classe de fonctions considerées dans l'etude du problème du Dirichlet, Fund. Math. 21 (1933), 129-150. | JFM | Zbl
,[51] Uber die erste Randwertaufgabe bei regularen Variationsproblemen I. Math. Zeit. 51 (1949), 712-7.51. | MR | Zbl
,[52] Uber partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeha, und uber die Transformation der Doppelintegrale, Math. Ann. 79 (1918), 340-359. | JFM
,[53] Ein Satz Uber mittlere Konvergence, Gottingen Nach. (Math.-Phys. Kl.) 1930), 30-35, | JFM
,[54] Theory of the Integral, See. Ed., Warsw-Lwow, 1937; English translation by L. C. Young. | JFM | Zbl
,[55] - , On the surfaces without tangent planes, Ann. of Math. 34 (1933), 114-124. | JFM | MR | Zbl
[56] Theorie des distributions I et II, Actitalites Sci. Ind. 1091 et 1122, Publ. Inst. Mate. Univ. Strasbourg 9 et 10, Paris 1950 of 1951. | Zbl
,[57] Differentiability and analyticity of solutions of double integral variational problems Ann. of Math. 48 (1947), 274-284. | MR | Zbl
,[58] Conditions for the existence of a minimum of double integrals in un unbounded region, Doklady Akad. Nank SSSR (N.S.) 8 (1951), 741-744 (Russian). | MR | Zbl
,[59] - , Regular double integrals of the calculus of variations in non-parametric form, Doklady Akad. Nauk SSSR (N.S.) 73 (1950), 891-894 (Russian). | MR
[60] - , Two dimensional problems of the calculus of variations in non-parartretric form, transformed into parametric form, Mat. Sbornik NS 94 (76) (1954), 385-406.
[61] - , On conditions of differentiability and analiticity of solutions of two dimensional problems of variations, Doklady Akad. Nauk SSSR (NS) 85 (1952), 273-275. | MR
[62] Existence of an absolute minimum of multiple integrals in the ealeulus of variations, Doklady Akad. Nank SSSR (N.S.) 102 (1955), 699-702. | MR | Zbl
,[63] - , Two dimensional problems of the calculus of variations, Uspehi Matem. Nauk (N.S.) 6 (1951), 16-101 (Russian). | MR
[64] Sur quelques evaluations concernant les familles des fonctions ayant des derivees a carré integrable, Comptes Rend. Acd, Sci. SSSR. N.S.I. 1936, 279-282. | JFM | Zbl
,[65] - , On a theorem of functional analysis, Mat. Sbornik N.S. 4 (1938). 471-497.
[66] Dirichlet's principle on manifolds, Studies in Mathematics and Mechanics presented to Richard von Mises, Academic Press (1954), 127-134. | Zbl
,[67] Sopra una classe di funzioni in due variabili. Applicazioni agli integrali doppi del caleolo delle variazioni, Giorn. Mat. Battaglini (4) 3 (79) (1950), 169-208. | MR | Zbl
,[68] - , Gli integrali doppi del calcolo delle variazioni in forma ordinaria, Atti A-ccad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 8 (1950), 21-26. | MR | Zbl
[69] - , Sistemi di equazioni di tipo ellittico a derivate parziali del primo ordine e proprietà degli estremi degli integrali multipli, Ricerche Mat. 1 (1952), 200-226. | MR | Zbl
[70] - , Problemi al contorno per equazioni di tipo ellittico e derivate parziali e questioni di calcolo delle variazioni connesse, Ann. Mat. Para Appl. (4) 33 (1952), 211-238 | MR | Zbl
[71] Sulla quadratura delle superficie, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (6) 3 (1926), 633-638. | JFM
,[72] - , Sui massimi e minimi assoluti del calcolo della variazione, Rend. Circ. Mat. Palermo 32 (1911), 297-337.
[73] - , Sul caso regolare nel calcolo delle variazioni, Rend. Circ. Mat. Palermo 35 (1913), 49-73.
[74] - , Sur une méthode directe du catcul des variations, Rend. Ciro. Mat. Palermo 39 (1915), 233-264.
[75] - , La semicontinuità nel calcolo delle variazioni, Rend. Ciro. Mat. Palermo 44 (1920), 167-249.
[76] - , Fondamenti del calcolo delle variazioni, Bologna, Zaniohelli, 3 vols.
[77] - , Sur la semi-continuité des intégrales doubles du calcul des variations, Acta Math. 53 (1929). 325-346. | JFM
[78] - , L'estremo assoluto degli integrali doppi, Ann. Sc. Norm. Pisa (2) 3 (1933), 89-130. | JFM | Numdam | Zbl
[79] Sur l'extension de la condition de Legendre du calcul des variations aux integrals multiples a plusieurs fonctions inconnues, Nederl. Akad. Wetensch. 50 (1947), 18-23. | MR | Zbl
,