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
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topLittman, 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
top- 1 Aronszajn, N. and Smith, K.T. - Functional spaces and functional completion, Ann. Inst. Fourier, 6. 1956, pp. 125-185. Zbl0071.33003MR80878
- 2 Brelot, M. — Eléments de la théorie classique du potentiel, ParisC. D. U., 1959. Zbl0084.30903MR106366
- 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 Deny. J., and Lions, L. - Les espaces de B. Levi, Ann. Inst. Fourier, 5, (1953-54), pp. 305-370. Zbl0065.09903
- 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 Fuglede, B. - Extremal length and functional completion, Acta. Math.98 (1957), pp. 171-219. Zbl0079.27703MR97720
- 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 Kellogg, O.D. — Foundations of potential theory, Springer (Berlin) 1929. Zbl55.0282.01MR222317JFM55.0282.01
- 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 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 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 Morrey, C.B. - Second order elliptic equations in several variables and Hölder continuity, Math. Zeit.72, pp. 146-164, (1959). Zbl0094.07802MR120446
- 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 Moser, J. - On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. Vol. XIV, pp. 577-591, (1961). Zbl0111.09302MR159138
- 15 Nash, J. - Continuity of the solutions of parabolic and elliptic equations, Amer. J. Math.80, pp. 931-954, (1958). Zbl0096.06902MR100158
- 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 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 Riesz, F., and B. Sz. Nagy - Lessons on Functional Analysis.
- 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 Schechter, M. — Negative Norms and Boundary Problems, Ann. of Math.72 (1960), pp. 581-593. Zbl0097.08401MR125333
- 21 Schwartz, L. - Théorie des Distributions, Paris. Zbl0037.07301
- 22 Stampacchia, G. - Régularisation des solutions de problèmes aux Limites elliptiques à données discontinues, Intern. Symp. on Lin. Spaces, Jerusalem (1960). Zbl0114.30403MR146512
- 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 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 Stampacchia, G. - On some regular multiple integral problems in the calculus of variations, to appear in Comm. Pure Appl. Math. Zbl0138.36903MR155209
- 26 Stampacchia, G. - Second order elliptic equations and boundary value problems, International Congress of Mathematians 1962, Stockholm. Zbl0137.06803MR176198
- 27 Tautz, G. - Reguläre Randpunkte beim verallgemeinertenDirichletschen Problem, 39 (1935), pp 532-559. Zbl0010.35603MR1545516JFM61.0531.02
- 28 Tautz, G. — Zur Theorie der ersten Randwertanfgabe, Math. Naohr.2 (1949), pp. 279-303. Zbl0037.07001MR32868
- 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 Wiener, N. - The Dirichlet problem, J. Math. and Phys. Vol. 3 (1924), pp. 127-146. Zbl51.0361.01JFM50.0646.02
- 31 Wiener, N. - Certain notions in potential theory, J. Math. and Phys. Vol. 3 (1924), pp. 24-51. Zbl50.0646.03JFM50.0646.03
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- Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
- Keith Miller, Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa
- Marco Biroli, Umberto Mosco, Wiener criterion for degenerate elliptic obstacle problem
- Marco Biroli, Umberto Mosco, Wiener criterion for degenerate elliptic obstacle problem
- Eduardo Casas, Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints
- Léopoldo Nachbin, Régularité des solutions des équations différentielles elliptiques
- Haïm Brézis, G. Stampacchia, Sur la régularité de la solution d'inéquations elliptiques
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