New Liouville theorems for linear second order degenerate elliptic equations in divergence form
Annales de l'I.H.P. Analyse non linéaire (2005)
- Volume: 22, Issue: 1, page 11-23
- ISSN: 0294-1449
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topMoschini, Luisa. "New Liouville theorems for linear second order degenerate elliptic equations in divergence form." Annales de l'I.H.P. Analyse non linéaire 22.1 (2005): 11-23. <http://eudml.org/doc/78644>.
@article{Moschini2005,
author = {Moschini, Luisa},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Linear degenerate elliptic equation; Liouville-type theorem; maximum principle},
language = {eng},
number = {1},
pages = {11-23},
publisher = {Elsevier},
title = {New Liouville theorems for linear second order degenerate elliptic equations in divergence form},
url = {http://eudml.org/doc/78644},
volume = {22},
year = {2005},
}
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
PB - Elsevier
VL - 22
IS - 1
SP - 11
EP - 23
LA - eng
KW - Linear degenerate elliptic equation; Liouville-type theorem; maximum principle
UR - http://eudml.org/doc/78644
ER -
References
top- [1] Ambrosio L., Cabré X., Entire solutions of semilinear elliptic equations in and a conjecture of De Giorgi, J. Amer. Math. Soc.13 (4) (2000) 725-739. Zbl0968.35041MR1775735
- [2] Barlow M.T., On the Liouville property for divergence form operators, Canad. J. Math.50 (3) (1998) 487-496. Zbl0912.31004MR1629807
- [3] Barlow M.T., Bass R.F., Gui C., The Liouville property and a conjecture of De Giorgi, CPAMLIII (2000) 1007-1038. Zbl1072.35526MR1755949
- [4] Berestycki H., Caffarelli L., Nirenberg L., Monotonicity for elliptic equations in unbounded Lipschitz domains, CPAML (1997) 1089-1111. Zbl0906.35035MR1470317
- [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. Zbl1079.35513MR1655510
- [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. Zbl0405.49001MR533166
- [7] De Giorgi E., Sulla differenziabilitá e analiticitá delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci.3 (1957) 25-43. Zbl0084.31901MR93649
- [8] Edmunds D.E., Peletier L.A., A Liouville theorem for degenerate elliptic equations, J. London Math. Soc. (2)7 (1973) 95-100. Zbl0262.35023MR328344
- [9] Finn R., Sur quelques généralisations du théorème de Picard, C. R. Acad. Sci. Paris Sér. A-B235 (1952) 596-598. Zbl0047.32201MR50668
- [10] Ghoussoub N., Gui C., On a conjecture of De Giorgi and some related problems, Math. Ann.311 (1998) 481-491. Zbl0918.35046MR1637919
- [11] Gilbarg D., Serrin J., On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math.4 (1955–1956) 309-340. Zbl0071.09701MR81416
- [12] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
- [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 , J. Analyse Math.39 (1981) 75-102. Zbl0477.35039MR632457
- [15] Karp L., 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. Zbl0477.35040MR632458
- [16] Kruzkov S.N., Certain properties of solutions to elliptic equations, Soviet. Math. Dokl.4 (1963) 686-695. Zbl0148.35701
- [17] Moser J., On Harnack's theorem for elliptic differential equations, CPAM14 (1961) 577-591. Zbl0111.09302MR159138
- [18] Nash J., Continuity of solutions of parabolic and elliptic equations, Amer. J. Math.80 (1958) 931-954. Zbl0096.06902MR100158
- [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. Zbl0383.35025MR481493
- [20] Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. Zbl0153.13602MR219861
- [21] O. Savin, Phase transitions: regularity of flat level sets, preprint. Zbl1180.35499
- [22] Trudinger N.S., On the regularity of generalized solutions of linear, non-uniformly elliptic equations, Arch. Rat. Mech. Anal.42 (1971) 51-62. Zbl0218.35035MR344656
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