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On harnack type inequalities and their application to quasilinear elliptic equations

1967; Wiley; Volume: 20; Issue: 4 Linguagem: Inglês

10.1002/cpa.3160200406

ISSN

1097-0312

Autores

Neil S. Trudinger,

Tópico(s)

Nonlinear Partial Differential Equations

Resumo

Communications on Pure and Applied MathematicsVolume 20, Issue 4 p. 721-747 Article On harnack type inequalities and their application to quasilinear elliptic equations Neil S. Trudinger, Neil S. TrudingerSearch for more papers by this author Neil S. Trudinger, Neil S. TrudingerSearch for more papers by this author First published: November 1967 https://doi.org/10.1002/cpa.3160200406Citations: 464AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 De Giorgi, E., Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, Ser. 3a, Vol. 3, 1957, pp. 25– 43. 2 John, F., and Nirenberg, L., On functions of bounded mean oscillation, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 415– 426. 3 Kruzkov, S. N., A priori estimates and some properties of solutions of elliptic and parabolic equations, Uspekhi Mat. Nauk, Vol. 18, 1963, pp. 215– 216. (In Russian.) 4 Kruzkov, S. N., Some estimates for generalized solutions of elliptic and parabolic equations of second order, Doklady Acad. Nauk SSSR, Vol. 150, 1963, pp. 748– 751. (In Russian.) 5 Ladyzhenskaya O. A. and Ural'tseva, N. N., Quasilinear elliptic equations and variational problems with many independent variables, Uspekhi Mat. Nauk, Vol. 16, 1961, pp. 19– 92. (In Russian. English Translation in Russian Math. Surveys, Vol. 16, 1961, pp. 17– 91.) 6 Ladyzhenskaya O. A. and Ural'tseva, N. N., Boundary value problems for linear and quasilinear parabolic equations, I, Izv. Akad. Nauk SSSR, Ser. Mat., Vol. 26, 1962, pp. 5– 52. II. Izv. Akad. Nauk SSSR, Ser. Mat., pp. 753– 780. III, Izv. Akad. Nauk SSSR, Ser. Mat., Vol. 27, 1963, pp. 161– 240. (In Russian.) 7 Ladyzhenskaya O. A. and Ural'tseva, N. N., Linear and Quasilinear Elliptic Equations, Izd. Nauka, Moscow, 1964. (In Russian.) 8 Ladyzhenskaya O. A. and Ural'tseva, N. N., On Hölder continuity of solutions and their derivatives of linear and quasilinear elliptic and parabolic equations, Trudy Steklov Inst., Leningrad, Vol. 73, 1964, pp. 172– 220. (In Russian.) 9 Morrey, C. B., Second order elliptic equations in several variables and Hölder continuity, Math. Z., Vol. 72, 1959, pp. 146– 164. 10 Morrey, C. B., Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966. 11 Moser, J., A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., Vol. 13, 1960, pp. 457– 468. 12 Moser, J., On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., Vol. 14, 1961, pp. 577– 591. 13 Moser, J., A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math., Vol. 17, 1964, pp. 101– 134. Correction to same paper, Comm. Pure Appl. Math., Vol. 20, 1967, pp. 231– 236 14 Nash, J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., Vol. 80, 1958, pp. 931– 954. 15 Schaefer, H., Über die Methode der a priori Schranken, Math. Ann., Vol. 129, 1955, pp. 415– 416. 16 Serrin, J., Local behaviour of solutions of quasilinear equations, Acta Math., Vol. 111, 1964, pp. 302– 347. 17 Serrin, J., Isolated singularities of solutions of quasilinear equations, Acta Math., Vol. 113, 1965, pp. 219– 240. 18 Stampacchia, G., Contributi alia regolarizzazione delle soluzioni dei problemi al contorno per equasioni del secondo ordine ellitiche, Ann. Scuola Norm Sup. Pisa, Ser. 3, Vol. 12, 1958, pp. 223– 244. 19 Stampacchia, G., Problemi al contorno ellittiche con dati discontinui dotati di soluzioni Holderiane, Ann. of Math., Vol. 51, 1960, pp. 1– 38. 20 Trudinger, N. S., Quasilinear elliptic partial differential equations in n variables, Stanford University, Dept. of Mathematics, July, 1966. 21 Trudinger, N. S., On imbeddings into Orlicz spaces and some applications, J. Math. Mech., Vol. 16, 1967, to appear. 22 Trudinger, N. S., The Dirichlet problem for quasilinear uniformly elliptic equations in n variables, Arch. Rat. Mech. Analysis, Vol. 24, 1967, to appear. Citing Literature Volume20, Issue4November 1967Pages 721-747 ReferencesRelatedInformation

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