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Gilbarg, D.; Serrin, James

On isolated singularities of solutions of second order elliptic differential equations. (English) Zbl 0071.09701

J. Anal. Math. 4, 309-340 (1956).
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Cited in 2 Reviews
Cited in 114 Documents

Keywords:

partial differential equations
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[1] S. Bernstein, Ueber ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus,Math. Zeit. 26 (1927), pp. 551–558. · JFM 53.0670.01 · doi:10.1007/BF01475472
[2] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications,Convegno Internazionale sulle Equazioni Derivate Parziali, 1954, pp. 111–140.
[3] L. Bers and L. Nirenberg, On linear and non-linear boundary value problems in the plane, same as preceding, pp. 141–167.
[4] M. Bôcher, Singular points of functions which satisfy partial differential equations of elliptic type.Bull. Amer. Math. Soc. 9 (1903), pp. 455–465. · JFM 35.0356.03 · doi:10.1090/S0002-9904-1903-01017-9
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[7] M. Gevrey, Sur certaines propriétés des fonctions harmoniques et leur extension aux équations aux dérivées partielles,C. R. Acad. Sci. Paris 183 (1926), pp. 546–548. · JFM 52.0482.03
[8] M. Gevrey, Sur une généralisation du principe des singularités positives de M. Picard,C. R. Acad. Sci. Paris 211 (1940), pp. 581–584. · JFM 66.0456.01
[9] P. Hartman and A. Wintner, On the local behavior of solutions of non-parabolic partial differential equations, I, II, III,Amer. J. of Math. 75 (1953), pp. 449–476; 76 (1954), pp. 351–361; 77 (1955), pp. 453–474. · Zbl 0052.32201 · doi:10.2307/2372496
[10] E. Hopf, Elementare Bettrachtungen ueber die Lösungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus,Sitzungsberichte Preuss. Akad. Wiss. 19 (1927), pp. 147–152. · JFM 53.0454.02
[11] E. Hopf, Bemerkungen zu einem Satze von S. Bernstein aus der theorie der elliptischen Differentialgleichungen,Math. Zeit. 29 (1928), pp. 744–745. · JFM 55.0289.01 · doi:10.1007/BF01180562
[12] C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations,Trans. Amer. Math. Soc. 43 (1938), pp. 126–166. · Zbl 0018.40501 · doi:10.1090/S0002-9947-1938-1501936-8
[13] C. B. Morrey, Second order elliptic systems of differential equations, in Contributions to the theory of partial differential equations,Ann. of Math. Studies No. 33, Princeton, 1954, pp. 101–159. · Zbl 0057.08301
[14] L. Nirenberg, On non-linear elliptic partial differential equations and Hölder continuity,Comm. on pure and appl. Math. 6 (1953), pp. 103–156. · Zbl 0050.09801 · doi:10.1002/cpa.3160060105
[15] J. Serrin, On the Harnck inequality for linear elliptic equations,J. d’ Analyse Math. (preceding in this issue).
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