Regular points for elliptic equations with discontinuous coefficients

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1963)

  • Volume: 17, Issue: 1-2, page 43-77
  • ISSN: 0391-173X

How to cite

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Littman, W., Stampacchia, G., and Weinberger, H. F.. "Regular points for elliptic equations with discontinuous coefficients." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.1-2 (1963): 43-77. <http://eudml.org/doc/83299>.

@article{Littman1963,
author = {Littman, W., Stampacchia, G., Weinberger, H. F.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {1-2},
pages = {43-77},
publisher = {Scuola normale superiore},
title = {Regular points for elliptic equations with discontinuous coefficients},
url = {http://eudml.org/doc/83299},
volume = {17},
year = {1963},
}

TY - JOUR
AU - Littman, W.
AU - Stampacchia, G.
AU - Weinberger, H. F.
TI - Regular points for elliptic equations with discontinuous coefficients
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1963
PB - Scuola normale superiore
VL - 17
IS - 1-2
SP - 43
EP - 77
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83299
ER -

References

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  1. 1 Aronszajn, N. and Smith, K.T. - Functional spaces and functional completion, Ann. Inst. Fourier, 6. 1956, pp. 125-185. Zbl0071.33003MR80878
  2. 2 Brelot, M. — Eléments de la théorie classique du potentiel, ParisC. D. U., 1959. Zbl0084.30903MR106366
  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). Zbl0084.31901MR93649
  4. 4 Deny. J., and Lions, L. - Les espaces de B. Levi, Ann. Inst. Fourier, 5, (1953-54), pp. 305-370. Zbl0065.09903
  5. 5 Frostman, O. - Les points irreguliers dans la théorie du potentiel et le critère de Wiener, Kungl. Fysiografiska Sällskapets J. Lund Förhandlingar9, (1939). Zbl0023.04501JFM65.0415.05
  6. 6 Fuglede, B. - Extremal length and functional completion, Acta. Math.98 (1957), pp. 171-219. Zbl0079.27703MR97720
  7. 7 Hervé, R.M. — Recherches axiomatique sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, Grenoble12 (1962), pp. 415-571. Zbl0101.08103MR139756
  8. 8 Kellogg, O.D. — Foundations of potential theory, Springer (Berlin) 1929. Zbl55.0282.01MR222317JFM55.0282.01
  9. 9 Kellogg, O.D. and Vasilesco F.A contribution to the theory of capacity, Amer. Journ. of Math51 (1929), pp. 515-526. Zbl55.0287.05MR1506733JFM55.0287.05
  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. Zbl64.0478.01JFM64.0478.01
  11. 11 Magknes, E., and Stampacchia, G. - I problemi al contorno per le equazioni differenziali di tipo ellittico, Ann. Sc. Norm. Sup. Pisa12 (1958), pp. 247-358. Zbl0082.09601MR123818
  12. 12 Morrey, C.B. - Second order elliptic equations in several variables and Hölder continuity, Math. Zeit.72, pp. 146-164, (1959). Zbl0094.07802MR120446
  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). Zbl0111.09301MR170091
  14. 14 Moser, J. - On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. Vol. XIV, pp. 577-591, (1961). Zbl0111.09302MR159138
  15. 15 Nash, J. - Continuity of the solutions of parabolic and elliptic equations, Amer. J. Math.80, pp. 931-954, (1958). Zbl0096.06902MR100158
  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. Zbl0003.20801JFM58.0493.03
  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. Zbl0152.31101MR145190
  20. 20 Schechter, M. — Negative Norms and Boundary Problems, Ann. of Math.72 (1960), pp. 581-593. Zbl0097.08401MR125333
  21. 21 Schwartz, L. - Théorie des Distributions, Paris. Zbl0037.07301
  22. 22 Stampacchia, G. - Régularisation des solutions de problèmes aux Limites elliptiques à données discontinues, Intern. Symp. on Lin. Spaces, Jerusalem (1960). Zbl0114.30403MR146512
  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. Zbl0082.09701MR125313
  24. 24 Stampacchia, G. - Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni holderiane, Annali di Matem. Vol 51, pp. 1-38, (1960). Zbl0204.42001MR126601
  25. 25 Stampacchia, G. - On some regular multiple integral problems in the calculus of variations, to appear in Comm. Pure Appl. Math. Zbl0138.36903MR155209
  26. 26 Stampacchia, G. - Second order elliptic equations and boundary value problems, International Congress of Mathematians 1962, Stockholm. Zbl0137.06803MR176198
  27. 27 Tautz, G. - Reguläre Randpunkte beim verallgemeinertenDirichletschen Problem, 39 (1935), pp 532-559. Zbl0010.35603MR1545516JFM61.0531.02
  28. 28 Tautz, G. — Zur Theorie der ersten Randwertanfgabe, Math. Naohr.2 (1949), pp. 279-303. Zbl0037.07001MR32868
  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. Zbl0123.07202MR145191
  30. 30 Wiener, N. - The Dirichlet problem, J. Math. and Phys. Vol. 3 (1924), pp. 127-146. Zbl51.0361.01JFM50.0646.02
  31. 31 Wiener, N. - Certain notions in potential theory, J. Math. and Phys. Vol. 3 (1924), pp. 24-51. Zbl50.0646.03JFM50.0646.03

Citations in EuDML Documents

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  1. Giuseppe Di Fazio, Hölder-continuity of solutions for some Schrödinger equations
  2. Umberto Mosco, Approximation of the solutions of some variational inequalities
  3. Annalisa Malusa, Harmonic measures of perforated domains
  4. Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
  5. Keith Miller, Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa
  6. Marco Biroli, Umberto Mosco, Wiener criterion for degenerate elliptic obstacle problem
  7. Marco Biroli, Umberto Mosco, Wiener criterion for degenerate elliptic obstacle problem
  8. Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
  9. Léopoldo Nachbin, Régularité des solutions des équations différentielles elliptiques
  10. Haïm Brézis, G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques

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