×
Serrin, J.

Local behavior of solutions of quasi-linear equations. (English) Zbl 0128.09101

Acta Math. 111, 247-302 (1964).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0128.09101

Cited in 8 Reviews
Cited in 553 Documents

Keywords:

partial differential equations
PDF BibTeX XML Cite
\textit{J. Serrin}, Acta Math. 111, 247--302 (1964; Zbl 0128.09101)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Carleson, L.,Selected problems on exceptional sets. Uppsala, 1961. (Mimeographed.) · Zbl 0114.05903
[2] Finn, R., Isolated singularities of solutions of non-linear partial differential equations.Trans. Amer. Math. Soc. 75 (1953), 385–404. · Zbl 0053.39205
[3] Gevrey, M., Sur une généralisation du principe des singularités positives de M. Picard.C. R. Acad. Sci. Paris, 211 (1940), 581–584. · Zbl 0025.05502
[4] Gilbarg, D., Some local properties of elliptic equations.Proceedings of Symposia on Pure Mathematics, Vol. 4, Partial Differential Equations, pp. 127–142. Amer. Math. Soc., Providence, R.I., 1961. · Zbl 0178.13001
[5] –, Boundary value problems for non-linear elliptic equations.Nonlinear Problems, pp. 151–160. Univ. of Wisconsin Press, Madison, 1963.
[6] Gilbarg, D. &Serrin, J., On isolated singularities of solutions of second order elliptic differential equations.J. d’Analyse Math., 4 (1955–1956), 309–340. · Zbl 0071.09701
[7] John, F. &Nirenberg, L., On functions of bounded mean oscillation.Comm. Pure. Appl. Math., 14 (1961), 415–426. · Zbl 0102.04302
[8] Ladyzhenskaya, O. A. &Uraltseva, N. N., Quasi-linear elliptic equations and variational problems with many independent variables.Uspehi Mat. Nauk, 16 (1961), 19–92; translated inRussian Math. Surveys, 16 (1961), 17–91.
[9] –, On the smoothness of weak solutions of quasi-linear equations in several variables and of variational problems.Comm. Pure Appl. Math., 14 (1961), 481–495. · Zbl 0131.09402
[10] Littman, W., Stampacchia, G. &Weinberger, H., Regular points for elliptic equations with discontinuous coefficients.Ann. Scuola Norm. Sup. Pisa, Ser. III, 17 (1963), 45–79. · Zbl 0116.30302
[11] Mazya, V. C., Some estimates for the solutions of second order elliptic equations.Dokl. Akad. Nauk SSSR, 137 (1961), 1057–1059; translated inSoviet Math. Dokl., 2 (1961), 413–415.
[12] –,p-conductance and theorems of imbedding certain function spaces into the space C.Dokl. Akad. Nauk SSSR, 140 (1961), 299–302; translated inSoviet Math. Dokl., 2 (1961), 1200–1203.
[13] Morrey, C. B., Jr., Second order elliptic equations and Hölder continuity.Math. Z., 72 (1959), 146–164. · Zbl 0094.07802
[14] –, Multiple integral problems in the calculus of variations and related topics.Ann. Scuola Norm. Sup. Pisa, 14 (1960), 1–62. · Zbl 0094.08104
[15] – Existence and differentiability theorems for variational problems for multiple integrals.Partial Differential Equations and Continuum Mechanics, pp. 241–270. Univ. of Wisconsin Press, Madison, 1961.
[16] Moser, J., A new proof of De giorgi’s theorem concerning the regularity problem for elliptic differential equations.Comm. Pure Appl. Math., 13 (1960), 457–468. · Zbl 0111.09301
[17] –, On Harnack’s theorem for elliptic differential equations.Comm. Pure Appl. Math., 14 (1961), 577–591. · Zbl 0111.09302
[18] Nirenberg, L., On elliptic partial differential equations.Ann. Scuola Norm. Sup. Pisa, 13 (1959), 1–48. · Zbl 0088.07601
[19] Picone, M., Sur la théorie d’un équation aux derivées partielles classique de la physique mathématique.C. R. Acad. Sci. Paris, 266 (1948), 1945–1947. Cf. also, Sulle singularitá delle soluzioni di una elassica equazione a derivate parziali delle fisica matematica.Atti 3{\(\deg\)} Congresso U.M.I., pp. 69–71. Rome, 1951. · Zbl 0030.30401
[20] 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 G. Polya, pp. 333–340. Stanford Univ. Press, Stanford, 1962.
[21] Serrin, J., Dirichlet’s principle in the calculus of variations.Proceedings of Symposia on Pure Mathematics, Vol. 4, Partial Differential Equations, pp. 17–22. Amer. Math. Soc., Providence, R.I., 1961. · Zbl 0178.14102
[22] –, A Harnack inequality for nonlinear equations.Bull. Amer. Math. Soc., 69 (1963), 481–486. · Zbl 0137.06902
[23] Stampacchia, G., Régularisation des solutions de problèmes aux limites elliptiques à données discontinues.Intern. Symposium on Linear Spaces, pp. 399–408. Jerusalem, 1960.
[24] –, Problemi al contorno ellittici, con dati discontinui dotati di soluzioni hölderiane.Ann. Pura Appl., 51 (1960), 1–38. · Zbl 0204.42001
[25] –, On some multiple integral problems in the calculus of variations.Comm. Pure Appl. Math., 16 (1963), 382–422.
[26] Wallin, H., A connection between {\(\alpha\)}-capacity andL p-classes of differentiable functions.Ark. Mat., 5 (1964), 331–341. · Zbl 0135.32401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.