Continuity of solutions of linear, degenerate elliptic equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)
- Volume: 6, Issue: 1, page 103-116
- ISSN: 0391-173X
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top- [1] E. De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.3 (1957), 25–43. Zbl0084.31901MR93649
- [2] E. De Giorgi, Congetture sulla continuità delle soluzioni di equazioni lineari ellittiche autoaggiunte a coefficienti illimitati, Unpublished, 1995.
- [3] B. Franchi, R. Serapioni and F. Cassano, Irregular solutions of linear degenerate elliptic equations Potential Anal. 9 (1998), 201–216. Zbl0919.35050MR1666899
- [4] D. Gilbarg and N. S. Trudinger, “Elliptic Partial Differential Equations of Second Order” 2nd ed., Springer-Verlag, New York, 1983. Zbl0361.35003MR737190
- [5] G. H. Hardy, J. E. Littlewood and G. Polya, “Inequalities”, 2nd ed., Cambridge University Press, Cambridge, 1952. Zbl0634.26008MR46395JFM60.0169.01
- [6] T. Iwaniec, P. Koskela and J. Onninen, Mappings of finite distortion: monotonicity and continuity, Invent. Math.144 (2001), 507–531. Zbl1006.30016MR1833892
- [7] O. A. Ladyzhenskaya and N. N. Ural’tseva, “Linear and Quasilinear Elliptic Equations”, Academic Press, New York, 1968. Zbl0164.13002MR244627
- [8] H. Lebesgue, Sur le problème de Dirichlet. Rend. Circ. Mat. Palermo27 (1907), 371–402. JFM38.0392.01
- [9] J. J. Manfredi, Weakly monotone functions, J. Geom. Anal.4 (1994), 393–402. Zbl0805.35013MR1294334
- [10] N. G. Meyers, An -estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 (1963), 189–206. Zbl0127.31904MR159110
- [11] C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc.43 (1938), 126–166. Zbl0018.40501MR1501936JFM64.0460.02
- [12] C. B. Morrey, Multiple integral problems in the calculus of variations and related topics. Univ. California Publ. Math. (N. S.) 1 (1943), 1–130. Zbl0063.04107MR11537
- [13] J. Moser, A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math.13 (1960), 457–468. Zbl0111.09301MR170091
- [14] J. Moser, On Harnack’s theorem for elliptic differential equations, Comm. Pure Appl. Math.14 (1961), 577–591. Zbl0111.09302MR159138
- [15] J. Nash, Continuity of solutions of elliptic and parabolic equations, Amer. J. Math.80 (1958), 931–954. Zbl0096.06902MR100158
- [16] J. Onninen and X. Zhong, A note on mappings of finite distortion: the sharp modulus of continuity, Michigan Math. J.53 (2005), 329–335. Zbl1086.30025MR2152704
- [17] L. C. Piccinini and S. Spagnolo, On the Hölder continuity of solutions of second order elliptic equations in two variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 391–402. Zbl0237.35028MR361422
- [18] J. Serrin, On the strong maximum principle for quasilinear second order differential inequalities, J. Funct. Anal.5 (1970), 184–193. Zbl0188.41701MR259328
- [19] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976), 353–372. Zbl0353.46018MR463908
- [20] N. S. Trudinger, On Harnack type inequalities and their application to quasilinear, elliptic equations, Comm. Pure Appl. Math.20 (1967), 721–747. Zbl0153.42703MR226198
- [21] N. S. Trudinger, On the regularity of generalized solutions of linear, non-uniformly elliptic equations, Arch. Rational Mech. Anal.42 (1971), 51–62. Zbl0218.35035MR344656
- [22] K. O. Widman, On the Hölder continuity of solutions of elliptic partial differential equations in two variables with coefficients in , Comm. Pure Appl. Math.22 (1969), 669–682. Zbl0183.11001MR251364