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Littman, W.; Stampacchia, G.; Weinberger, H. F.

Regular points for elliptic equations with discontinuous coefficients. (English) Zbl 0116.30302

Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 17, 43-77 (1963).
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Cited in 4 Reviews
Cited in 329 Documents

MathOverflow Questions:

Fundamental solution of an elliptic PDE in divergence form with non-symmetric matrix
Proof of Littman-Stampacchia-Weinberger theorem on the fundamental solution for elliptic PDEs
Reference Request for global Hölder continuity of solutions to elliptic PDEs
References for Green functions of \(\nabla \cdot a \nabla\) on a domain with \(a \in L^\infty\)

Keywords:

partial differential equations
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References:

[1] 1 Aronszajn , N. and Smith , K.T. - Functional spaces and functional completion , Ann. Inst. Fourier , 6 . 1956 , pp. 125 - 185 . Numdam | MR 80878 | Zbl 0071.33003 · Zbl 0071.33003 · doi:10.5802/aif.63
[2] 2 Brelot , M. - Eléments de la théorie classique du potentiel , Paris C. D. U. , 1959 . MR 106366 | Zbl 0084.30903 · Zbl 0084.30903
[3] 3 De Giorgi , E. - Sulla differentiabilità e l’analiticità delle estremali degli integrali multipli regolari , Mem. Accad. Sci. Torino , S. III , Parte I, pp. 25 - 43 , ( 1957 ). MR 93649 | Zbl 0084.31901 · Zbl 0084.31901
[4] 4 Deny . J. , and Lions , L. - Les espaces de B. Levi , Ann. Inst. Fourier , 5 , ( 1953 -54), pp. 305 - 370 . Numdam | Zbl 0065.09903 · Zbl 0065.09903 · doi:10.5802/aif.55
[5] 5 Frostman , O. - Les points irreguliers dans la théorie du potentiel et le critère de Wiener , Kungl. Fysiografiska Sällskapets J. Lund Förhandlingar 9 , ( 1939 ). Zbl 0023.04501 | JFM 65.0415.05 · Zbl 0023.04501
[6] 6 Fuglede , B. - Extremal length and functional completion , Acta. Math. 98 ( 1957 ), pp. 171 - 219 . MR 97720 | Zbl 0079.27703 · Zbl 0079.27703 · doi:10.1007/BF02404474
[7] 7 Hervé , R.M. - Recherches axiomatique sur la théorie des fonctions surharmoniques et du potentiel , Ann. Inst. Fourier , Grenoble 12 ( 1962 ), pp. 415 - 571 . Numdam | MR 139756 | Zbl 0101.08103 · Zbl 0101.08103 · doi:10.5802/aif.125
[8] 8 Kellogg , O.D. - Foundations of potential theory , Springer ( Berlin ) 1929 . MR 222317 | JFM 55.0282.01 · JFM 55.0282.01
[9] 9 Kellogg , O.D. and Vasilesco F. A contribution to the theory of capacity , Amer. Journ. of Math 51 ( 1929 ), pp. 515 - 526 . MR 1506733 | JFM 55.0287.05 · JFM 55.0287.05
[10] 10 La Vallée Poussin , C. De - Points irreguliers. Détermination des masses par les potentiels , Académie royale de Belgique. Bull. Classe des Sciences s. 5 t. 24 ( 1938 ), pp. 368 - 384 and 672 - 689 . JFM 64.0478.01 · JFM 64.0478.01
[11] 11 Magknes , E. , and Stampacchia , G. - I problemi al contorno per le equazioni differenziali di tipo ellittico , Ann. Sc. Norm. Sup. Pisa 12 ( 1958 ), pp. 247 - 358 . Numdam | MR 123818 | Zbl 0082.09601 · Zbl 0082.09601
[12] 12 Morrey , C.B. - Second order elliptic equations in several variables and Hölder continuity , Math. Zeit. 72 , pp. 146 - 164 , ( 1959 ). MR 120446 | Zbl 0094.07802 · Zbl 0094.07802 · doi:10.1007/BF01162944
[13] 13 Moser , J. - A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations , Comm. Pure Appl. Math. vol. 13 . pp. 457 - 468 , ( 1960 ). MR 170091 | Zbl 0111.09301 · Zbl 0111.09301 · doi:10.1002/cpa.3160130308
[14] 14 Moser , J. - On Harnack’s theorem for elliptic differential equations , Comm. Pure Appl. Math. Vol. XIV , pp. 577 - 591 , ( 1961 ). MR 159138 | Zbl 0111.09302 · Zbl 0111.09302 · doi:10.1002/cpa.3160140329
[15] 15 Nash , J. - Continuity of the solutions of parabolic and elliptic equations , Amer. J. Math. 80 , pp. 931 - 954 , ( 1958 ). MR 100158 | Zbl 0096.06902 · Zbl 0096.06902 · doi:10.2307/2372841
[16] 16 Ole , O.A. - On the Dirichlet problem for equations of elliptic type (Russ.) , Math. Sb. N. S. 24 ( 66 ), ( 1949 ), pp. 3 - 14 .
[17] 17 Püschel , W. - Die erste Randwertaufgabe der allgemeimen selbstadjungierten elliptischen Differentialgleichung zweiter Ordnung für beliebige Gebiete , Math. Zeit. 34 ( 1931 ), pp. 535 - 553 . Zbl 0003.20801 | JFM 58.0493.03 · Zbl 0003.20801 · doi:10.1007/BF01180608
[18] 18 Riesz , F. , and B. Sz. Nagy - Lessons on Functional Analysis .
[19] 19 Royden , H. - The growth of a fundamental solution of an elliptic divergence structure equation , Studies in Mathematical Analysis and Related Topics: Essays in Honor of George Polya , Stanford , 1962 , pp. 333 - 340 . MR 145190 | Zbl 0152.31101 · Zbl 0152.31101
[20] 20 Schechter , M. - Negative Norms and Boundary Problems , Ann. of Math. 72 ( 1960 ), pp. 581 - 593 . MR 125333 | Zbl 0097.08401 · Zbl 0097.08401 · doi:10.2307/1970230
[21] 21 Schwartz , L. - Théorie des Distributions , Paris . · Zbl 0962.46025
[22] 22 Stampacchia , G. - Régularisation des solutions de problèmes aux Limites elliptiques à données discontinues , Intern. Symp. on Lin. Spaces , Jerusalem ( 1960 ). MR 146512 | Zbl 0114.30403 · Zbl 0114.30403
[23] 23 Stampacchia , G. - Contributi alla regolarizzazione delle soluzioni dei problemi al contorno per equazioni del secondo ordine ellittiche , Annali Scuola Normale Superiore di Pisa , S. III , Vol. XII ( 1958 ), pp. 223 - 245 . Numdam | MR 125313 | Zbl 0082.09701 · Zbl 0082.09701
[24] 24 Stampacchia , G. - Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni holderiane , Annali di Matem. Vol 51 , pp. 1 - 38 , ( 1960 ). MR 126601 | Zbl 0204.42001 · Zbl 0204.42001 · doi:10.1007/BF02410941
[25] 25 Stampacchia , G. - On some regular multiple integral problems in the calculus of variations , to appear in Comm. Pure Appl. Math. MR 155209 | Zbl 0138.36903 · Zbl 0138.36903 · doi:10.1002/cpa.3160160403
[26] 26 Stampacchia , G. - Second order elliptic equations and boundary value problems , International Congress of Mathematians 1962 , Stockholm . MR 176198 | Zbl 0137.06803 · Zbl 0137.06803
[27] 27 Tautz , G. - Reguläre Randpunkte beim verallgemeinerten Dirichletschen Problem , 39 ( 1935 ), pp 532 - 559 . MR 1545516 | Zbl 0010.35603 | JFM 61.0531.02 · Zbl 0010.35603 · doi:10.1007/BF01201372
[28] 28 Tautz , G. - Zur Theorie der ersten Randwertanfgabe , Math. Naohr. 2 ( 1949 ), pp. 279 - 303 . MR 32868 | Zbl 0037.07001 · Zbl 0037.07001 · doi:10.1002/mana.19490020505
[29] 29 Weinberger , H.F. - Symmetrization in uniformly elliptic problems , Studies in Mathematioal Analysis and Related Topics: Essays in Honor of George Polya , Stanford ( 1962 ) pp. 424 - 428 . MR 145191 | Zbl 0123.07202 · Zbl 0123.07202
[30] 30 Wiener , N. - The Dirichlet problem , J. Math. and Phys . Vol. 3 ( 1924 ), pp. 127 - 146 . JFM 50.0646.02 · JFM 50.0646.02
[31] 31 Wiener , N. - Certain notions in potential theory , J. Math. and Phys. Vol. 3 ( 1924 ), pp. 24 - 51 . JFM 50.0646.03 · JFM 50.0646.03
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