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Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative Characteristic Form
Boundary Value Problems volume 2007, Article number: 048232 (2007)
Abstract
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.
References
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
Kogoj AE, Lanconelli E: One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations. In Geometric Analysis of PDE and Several Complex Variables, Contemporary Math.. Volume 368. American Mathematical Society, Providence, RI, USA; 2005:305–312.
Kogoj AE, Lanconelli E: Liouville theorems in halfspaces for parabolic hypoelliptic equations. Ricerche di Matematica 2006,55(2):267–282.
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.
Luo X: Liouville's theorem for homogeneous differential operators. Communications in Partial Differential Equations 1997,22(11–12):1837–1848. 10.1080/03605309708821322
Lanconelli E, Pascucci A: Superparabolic functions related to second order hypoelliptic operators. Potential Analysis 1999,11(3):303–323. 10.1023/A:1008689803518
Amano K: Maximum principles for degenerate elliptic-parabolic operators. Indiana University Mathematics Journal 1979,28(4):545–557. 10.1512/iumj.1979.28.28038
Glagoleva RJa: Liouville theorems for the solution of a second order linear parabolic equation with discontinuous coefficients. Matematicheskie Zametki 1969,5(5):599–606.
Bear HS: Liouville theorems for heat functions. Communications in Partial Differential Equations 1986,11(14):1605–1625. 10.1080/03605308608820476
Bonfiglioli A, Lanconelli E: Liouville-type theorems for real sub-Laplacians. Manuscripta Mathematica 2001,105(1):111–124. 10.1007/PL00005872
Lanconelli E, Polidoro S: On a class of hypoelliptic evolution operators. Rendiconti Seminario Matematico Università e Politecnico di Torino 1994,52(1):29–63.
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
Kogoj AE, Lanconelli E: Link of groups and applications to PDE's. to appear in Proceedings of the American Mathematical Society
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Kogoj, A.E., Lanconelli, E. Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative Characteristic Form. Bound Value Probl 2007, 048232 (2007). https://doi.org/10.1155/2007/48232
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DOI: https://doi.org/10.1155/2007/48232