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Liouville theorems for a class of linear second-order operators with nonnegative characteristic form. (English) Zbl 1158.35338

Summary: We report on some Liouville-type theorems for a class of linear second-order partial differential equation with nonnegative characteristic form. The theorems we show improve our previous results.

MSC:

35H10 Hypoelliptic equations
35B45 A priori estimates in context of PDEs
35J15 Second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs

References:

[1] Kogoj AE, Lanconelli E: An invariant Harnack inequality for a class of hypoelliptic ultraparabolic equations.Mediterranean Journal of Mathematics 2004,1(1):51-80. 10.1007/s00009-004-0004-8 · Zbl 1150.35354 · doi:10.1007/s00009-004-0004-8
[2] Kogoj, AE; Lanconelli, E., One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations, No. 368, 305-312 (2005), Providence, RI, USA · Zbl 1073.35068 · doi:10.1090/conm/368/06786
[3] Kogoj AE, Lanconelli E: Liouville theorems in halfspaces for parabolic hypoelliptic equations.Ricerche di Matematica 2006,55(2):267-282. · Zbl 1121.35030 · doi:10.1007/s11587-006-0015-9
[4] Lanconelli E: A polynomial one-side Liouville theorems for a class of real second order hypoelliptic operators.Rendiconti della Accademia Nazionale delle Scienze detta dei XL 2005, 29: 243-256.
[5] Luo X: Liouville’s theorem for homogeneous differential operators.Communications in Partial Differential Equations 1997,22(11-12):1837-1848. 10.1080/03605309708821322 · Zbl 0908.35027 · doi:10.1080/03605309708821322
[6] Lanconelli E, Pascucci A: Superparabolic functions related to second order hypoelliptic operators.Potential Analysis 1999,11(3):303-323. 10.1023/A:1008689803518 · Zbl 0940.35054 · doi:10.1023/A:1008689803518
[7] Amano K: Maximum principles for degenerate elliptic-parabolic operators.Indiana University Mathematics Journal 1979,28(4):545-557. 10.1512/iumj.1979.28.28038 · Zbl 0423.35023 · doi:10.1512/iumj.1979.28.28038
[8] Glagoleva RJa: Liouville theorems for the solution of a second order linear parabolic equation with discontinuous coefficients.Matematicheskie Zametki 1969,5(5):599-606. · Zbl 0175.39702
[9] Bear HS: Liouville theorems for heat functions.Communications in Partial Differential Equations 1986,11(14):1605-1625. 10.1080/03605308608820476 · Zbl 0651.35035 · doi:10.1080/03605308608820476
[10] Bonfiglioli A, Lanconelli E: Liouville-type theorems for real sub-Laplacians.Manuscripta Mathematica 2001,105(1):111-124. 10.1007/PL00005872 · Zbl 1016.35014 · doi:10.1007/PL00005872
[11] Lanconelli E, Polidoro S: On a class of hypoelliptic evolution operators.Rendiconti Seminario Matematico Università e Politecnico di Torino 1994,52(1):29-63. · Zbl 0811.35018
[12] Priola E, Zabczyk J: Liouville theorems for non-local operators.Journal of Functional Analysis 2004,216(2):455-490. 10.1016/j.jfa.2004.04.001 · Zbl 1063.31003 · doi:10.1016/j.jfa.2004.04.001
[13] Kogoj AE, Lanconelli E: Link of groups and applications to PDE’s. to appear in Proceedings of the American Mathematical Society · Zbl 1170.35034
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