New Liouville theorems for linear second order degenerate elliptic equations in divergence form

Moschini, Luisa

doi:10.1016/j.anihpc.2004.03.001

Moschini, Luisa

Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 22 (2005) no. 1, pp. 11-23

MR Zbl

DOI : 10.1016/j.anihpc.2004.03.001

@article{AIHPC_2005__22_1_11_0,
     author = {Moschini, Luisa},
     title = {New {Liouville} theorems for linear second order degenerate elliptic equations in divergence form},
     journal = {Annales de l'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {11--23},
     year = {2005},
     publisher = {Elsevier},
     volume = {22},
     number = {1},
     doi = {10.1016/j.anihpc.2004.03.001},
     mrnumber = {2114409},
     zbl = {02141609},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.03.001/}
}

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Moschini, Luisa. New Liouville theorems for linear second order degenerate elliptic equations in divergence form. Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 22 (2005) no. 1, pp. 11-23. doi: 10.1016/j.anihpc.2004.03.001

Bibliographie
Cité par

[1] Ambrosio L., Cabré X., Entire solutions of semilinear elliptic equations in $R^{3}$ and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (4) (2000) 725-739. | Zbl | MR

[2] Barlow M.T., On the Liouville property for divergence form operators, Canad. J. Math. 50 (3) (1998) 487-496. | Zbl | MR

[3] Barlow M.T., Bass R.F., Gui C., The Liouville property and a conjecture of De Giorgi, CPAM LIII (2000) 1007-1038. | Zbl | MR

[4] Berestycki H., Caffarelli L., Nirenberg L., Monotonicity for elliptic equations in unbounded Lipschitz domains, CPAM L (1997) 1089-1111. | Zbl | MR

[5] Berestycki H., Caffarelli L., Nirenberg L., Further qualitative properties for elliptic equations in unbounded domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 69-94. | Zbl | MR | Numdam

[6] De Giorgi E., Convergence problems for functionals and operators, in: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, Bologna, 1979, pp. 131-188. | Zbl | MR

[7] De Giorgi E., Sulla differenziabilitá e analiticitá delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. 3 (1957) 25-43. | Zbl | MR

[8] Edmunds D.E., Peletier L.A., A Liouville theorem for degenerate elliptic equations, J. London Math. Soc. (2) 7 (1973) 95-100. | Zbl | MR

[9] Finn R., Sur quelques généralisations du théorème de Picard, C. R. Acad. Sci. Paris Sér. A-B 235 (1952) 596-598. | Zbl | MR

[10] Ghoussoub N., Gui C., On a conjecture of De Giorgi and some related problems, Math. Ann. 311 (1998) 481-491. | Zbl | MR

[11] Gilbarg D., Serrin J., On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4 (1955-1956) 309-340. | Zbl | MR

[12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | Zbl | MR

[13] A. Grigor'yan, L. Saloff-Coste, Stability results for Harnack inequalities, preprint.

[14] Karp L., Asymptotic behavior of solutions of elliptic equations I: Liouville-type theorems for linear and nonlinear equations on $R^{n}$ , J. Analyse Math. 39 (1981) 75-102. | Zbl | MR

[15] Karp L., Asymptotic behavior of solutions of elliptic equations II: Analogues of Liouville’s theorem for solutions of inequalities on $R^{n}, n \geq 3$ , J. Analyse Math. 39 (1981) 103-115. | Zbl | MR

[16] Kruzkov S.N., Certain properties of solutions to elliptic equations, Soviet. Math. Dokl. 4 (1963) 686-695. | Zbl

[17] Moser J., On Harnack's theorem for elliptic differential equations, CPAM 14 (1961) 577-591. | Zbl | MR

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

[19] Peletier L.A., Serrin J., Gradient bounds and Liouville theorems for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978) 65-104. | Zbl | MR | Numdam

[20] Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. | Zbl | MR

[21] O. Savin, Phase transitions: regularity of flat level sets, preprint.

[22] Trudinger N.S., On the regularity of generalized solutions of linear, non-uniformly elliptic equations, Arch. Rat. Mech. Anal. 42 (1971) 51-62. | Zbl | MR

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