@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'I.H.P. Analyse non lin\'eaire}, pages = {11--23}, publisher = {Elsevier}, volume = {22}, number = {1}, year = {2005}, doi = {10.1016/j.anihpc.2004.03.001}, mrnumber = {2114409}, zbl = {02141609}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.03.001/} }
TY - JOUR AU - Moschini, Luisa TI - New Liouville theorems for linear second order degenerate elliptic equations in divergence form JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 11 EP - 23 VL - 22 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2004.03.001/ DO - 10.1016/j.anihpc.2004.03.001 LA - en ID - AIHPC_2005__22_1_11_0 ER -
%0 Journal Article %A Moschini, Luisa %T New Liouville theorems for linear second order degenerate elliptic equations in divergence form %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 11-23 %V 22 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2004.03.001/ %R 10.1016/j.anihpc.2004.03.001 %G en %F AIHPC_2005__22_1_11_0
Moschini, Luisa. New Liouville theorems for linear second order degenerate elliptic equations in divergence form. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 1, pp. 11-23. doi : 10.1016/j.anihpc.2004.03.001. http://www.numdam.org/articles/10.1016/j.anihpc.2004.03.001/
[1] Entire solutions of semilinear elliptic equations in and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (4) (2000) 725-739. | MR | Zbl
, ,[2] On the Liouville property for divergence form operators, Canad. J. Math. 50 (3) (1998) 487-496. | MR | Zbl
,[3] The Liouville property and a conjecture of De Giorgi, CPAM LIII (2000) 1007-1038. | MR | Zbl
, , ,[4] Monotonicity for elliptic equations in unbounded Lipschitz domains, CPAM L (1997) 1089-1111. | MR | Zbl
, , ,[5] Further qualitative properties for elliptic equations in unbounded domains, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 69-94. | Numdam | MR | Zbl
, , ,[6] Convergence problems for functionals and operators, in: Proc. Int. Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, Bologna, 1979, pp. 131-188. | MR | Zbl
,[7] Sulla differenziabilitá e analiticitá delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. 3 (1957) 25-43. | MR | Zbl
,[8] A Liouville theorem for degenerate elliptic equations, J. London Math. Soc. (2) 7 (1973) 95-100. | MR | Zbl
, ,[9] Sur quelques généralisations du théorème de Picard, C. R. Acad. Sci. Paris Sér. A-B 235 (1952) 596-598. | MR | Zbl
,[10] On a conjecture of De Giorgi and some related problems, Math. Ann. 311 (1998) 481-491. | MR | Zbl
, ,[11] On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4 (1955-1956) 309-340. | MR | Zbl
, ,[12] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR | Zbl
, ,[13] A. Grigor'yan, L. Saloff-Coste, Stability results for Harnack inequalities, preprint.
[14] Asymptotic behavior of solutions of elliptic equations I: Liouville-type theorems for linear and nonlinear equations on , J. Analyse Math. 39 (1981) 75-102. | MR | Zbl
,[15] Asymptotic behavior of solutions of elliptic equations II: Analogues of Liouville’s theorem for solutions of inequalities on , J. Analyse Math. 39 (1981) 103-115. | MR | Zbl
,[16] Certain properties of solutions to elliptic equations, Soviet. Math. Dokl. 4 (1963) 686-695. | Zbl
,[17] On Harnack's theorem for elliptic differential equations, CPAM 14 (1961) 577-591. | MR | Zbl
,[18] Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958) 931-954. | MR | Zbl
,[19] Gradient bounds and Liouville theorems for quasilinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978) 65-104. | Numdam | MR | Zbl
, ,[20] Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. | MR | Zbl
, ,[21] O. Savin, Phase transitions: regularity of flat level sets, preprint.
[22] On the regularity of generalized solutions of linear, non-uniformly elliptic equations, Arch. Rat. Mech. Anal. 42 (1971) 51-62. | MR | Zbl
,Cité par Sources :