Équations elliptiques du second ordre à coefficients discontinus

Stampacchia, Guido

Séminaire Jean Leray, no. 3 (1963-1964), pp. 1-77.

[1] Aronson, On the Green's function for second order parabolic differential équations with discontinuous coefficients. Bull. of the Amer. Math. Soc. vol. 69 (1963) pp.841-847. | MR | Zbl

[2] E. De Giorgi, Sulla differenziabilità e l'analicità delle estremali degli integrali multipli regolari. Mem. Accad. Sc. Torino (3) 3 (1957) pp. 25-43. | MR | Zbl

[3] D. Gilbarg, Boundary value problems for nonlinear elliptic equations in n variables. Symposium on Nonlinear Problems, Madison, Wisconsin, (1962). | MR | Zbl

[4] Guglielmino, Sulla regolarizzazione delle soluzioni deboli dei problemi al contorno per operatori parabolici. Ricerche di Matem., vol. XII (1963) pp.44-66. | MR | Zbl

[5] Hardy, Littlewood and Polya. Inequalities, Cambridge, 1952. | MR | Zbl

[6] F. John and L. Nirenberg, On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1960), pp.93-140. | MR | Zbl

[7] O.A. Ladyzenskaia et N.N. Uralt'Seva, Quasi-linear elliptic equations and variational problems with many independent variables. Russian Math. Surveys, London Math. Soc. (16) 1 (1961), pp. 17-91. | Zbl

[8] ----- On the smoothness of weak solutions of quasi-linear équations in several variables and of variational problems. Comm. Pure Appl. Math. 14 (1961), pp. 481-495. | MR | Zbl

[9] ----- A boundary-value problem for linear and quasi-linear parabolic equations, I, Izv. Akad. Nauk SSSR Sez. Mat. 26 (1962), pp.5-52, (Russian). | Zbl

[10] W. Littman, G. Stampacchia and H. Weinberg, Regular points for elliptic équations with discontinuous coefficients. Ann. Sc. Norm. Sup. Pira - S III (XVII) (1963), pp. 45-79. | Numdam | MR | Zbl

[11] N. Meyers, An Lp estimate for the gradient of solutions of second order elliptic divergence structure équations. Ann. Sc. Norm. Sup. Pisa 17 (1963), pp. 189-206. | Numdam | MR | Zbl

[12] C.B. Morrey, Second order elliptic équations in several variables and Hölder continuity. Math. Z. 72 (1952), pp. 146-164. | MR | Zbl

[13] C.B. Morrey, Existence and differentiability theorem for variational problems for multiple integrals - Conf. on Partial Diff. Equations and Continuum Mechanics. Univ. of Wisconsin Press, Madison, Wisc. 1961. | MR | Zbl

[ 14 ] J. Moser, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differontial equations. Comm. Pure Appl. Math. 13 (1960), pp. 457-468. | MR | Zbl

[15] ----- On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. XIV (1961), pp. 577-591. | Zbl

[16] ----- A Harnack inequality for Parabolic Differential Equations. Comm. Pure Appl. Math., vol. XVII, pp. 101-134 (1964). | MR | Zbl

[17] C. Miranda, Alcune osservazioni sulla maggiorazione in L delle soluzioni deboli delle equazioni ellittiche del secondo ordine. Ann. di Matem. t.61 (1963) pp. 151-168. | MR | Zbl

[18] ----- Sull' equazioni ellittiche del secondo ordine di tipo non variazionale, a coefficienti discontinui. Ann. di Matem. s. IV, t.LXIII, pp. 353-386 (1963). | MR | Zbl

[19] J. Nash, Continuity of the solutions of parabolic and elliptic equations. Amer. J. Math. 80 (1958), pp.931-954. | MR | Zbl

[20] L. Schwartz, Théorie des distributions, Paris, Hermann. | MR | Zbl

[21] J. Serrin, Pathological Solutions of Elliptic differential equations, Ann. Sc. Norm. Sup. Pisa (à paraître). | Numdam | Zbl

[22] ----- Local behavior of solutions of quasi-linear equations (à paraître). | Zbl

[231] ---- Contributi alla regolarizazziono delle soluzioni dei problemi al contorno per equazioni del secondo ordino ellittiche. Ann. Sc. Norm. Sup. Pisa (III) 12 (1958), pp.223-244 (Appendice). | Numdam | Zbl

[24] ----- Problemi al contorno ellittici, con dati discontinui, dotati di soluzioni holderiane. Ann. Mat. Pura Appl. (IV) 51(1960), pp. 1-38. | MR | Zbl

[25] ----- Régularisation des solutions de problèmes aux limites elliptiques à données discontinues. Intern. Symp. Lin. Spaces, Jerusalem, 1960. | Zbl

[26] G. Stampacchia, Equations elliptiques à données discontinues. Séminaire Schwartz, t.5, 1960-61, Equations aux dérivées partielles et interpolation, n.4, 16 p. | Numdam

[27] ----- Some limit cases of Lp-estimates for solutions of second order elliptic équations. Comm. Pure Appl. Math. 16 (1963). | Zbl

[28] ----- On some regular Multiple intégral Problems in the Calculus of Variations. Comm. Pure Appl. Math. vol. XVI (1963) | MR | Zbl

[29] ----- Formes bilinéaires coercitives sur les ensembles convexes. Comptes-rendus Acad.des Sci. de Paris (séance du 27 avril). | Zbl

[30] Zygmund A., On a theorem of Marcinkiewicz concerning interpolation of opérations. J. Math. Pures Appl. 35 (1956), pp. 223-248. | MR | Zbl

I C.B. Morrey, Some recent developments in the theory of partial differential equations. Bull. Amer. Math. Soc. t.68, 1962, pp.279-297. | Zbl

II ----- Des résultats récents du calcul des variations, Séminaire sur les équations aux dérivées partielles, 1961-62, n°5, 62 p. (Collège de France, nov. 1961-mai 1962).

III L. Nachbin, Régularité des solutions des équations différentielles elliptiques, Séminaire Bourbaki, 15e année, 1962-63, n°258. | Numdam | Zbl

IV L. Nirenberg, Some aspects of linear and non linear partial differential equations. Proceedings of the International Congress of mathematicians (1962), Stockholm, pp. 147-162. | MR | Zbl

V Stampacchia G. Second order elliptic equations and boundary value problems, Proceedings of the International Congress of mathematicians (1962), Stockholm, pp. 405-413. | MR | Zbl