Journal of Mathematical Sciences: Advances and Applications[1] M. E. Amendola, L. Rossi and A. Vitolo, Harnack inequalities and
ABP estimates for nonlinear second order elliptic equations in
unbounded domains, Abstr. Appl. Anal., 2008, Article ID 178534, 19
pp.
[2] H. Berestycki, L. A. Caffarelli and L. Nirenberg, Inequalities for
second-order elliptic equations with applications to unbounded domains
I, A celebration of John F. Nash, Duke Math. J. 81(2) (1996),
467-494.
[3] H. Berestycki, L. A. Caffarelli and L. Nirenberg, Monotonicity for
elliptic equations in unbounded Lipschitz domains, Comm. Pure Appl.
Math. 50(11) (1997), 1089-1111.
[4] H. Berestycki, L. Caffarelli and L. Nirenberg, Further qualitative
properties for elliptic equations in unbounded domains, Dedicated to
Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25(1-2)
(1998), 69-94.
[5] H. Berestycki, L. Nirenberg and S. R. S. Varadhan, The principal
eigenvalue and maximum principle for second-order elliptic operators
in general domains, Comm. Pure Appl. Math. 47 (1994).
[6] J. Busca, Existence results for Bellman equations and maximum
principles in unbounded domains, Comm. Partial Differential Equations
24 (1999), 2023-2042.
[7] X. Cabré, On the Alexandroff-Bakelman-Pucci estimate and
reversed Hölder inequality for solutions of elliptic and parabolic
equations, Comm. Pure Appl. Math. 48 (1995), 539-570.
[8] V. Cafagna and A. Vitolo, On the maximum principle for
second-order elliptic operators in unbounded domains, C. R. Acad. Sci.
Paris, Ser. I (2002), 334.
[9] L. A. Caffarelli, Elliptic second order equations, Rend. Semin.
Mat. Fis. Milano 57 (1988), 253-284.
[10] L. A. Caffarelli and X. Cabré, Fully nonlinear elliptic
equations, Amer Math. Soc. Colloq. Publ. 43, (1995).
[11] I. Capuzzo Dolcetta, Viscosity solutions Boll. Un. Mat. Ital.
Sez. B Art. Ric. Mat. 4(1) (2001), 1-29.
[12] I. Capuzzo Dolcetta, F. Leoni and A. Vitolo, The
Alexandrov-Bakelman-Pucci weak maximum principle for fully nonlinear
equations in unbounded domains, Comm. Partial Diff. Eqns. 30 (2005),
1863-1881.
[13] I. Capuzzo Dolcetta and A. Vitolo, A qualitative
Phragmèn-Lindelöf theorem for fully nonlinear elliptic
equations, Preprint (2006).
[14] I. Capuzzo Dolcetta and A. Vitolo, Local and global estimates for
viscosity solutions of fully nonlinear elliptic equations, Dynamics of
Continuous, Discrete and Impulsive Systems, Series A 14 S2 (2007),
11-16.
[15] M. G. Crandall, H. Ishii and P. L. Lions, User’s guide to
viscosity solutions of second order partial differential equations,
Bull. Amer. Math. Soc. 27(1) (1992).
[16] D. Gilbarg, The Phragmèn-Lindelöf theorem for elliptic
partial differential equations, J. Rat. Mech. Anal. 1 (1952),
411-417.
[17] D. Gilbarg and N. S. Trudinger, Elliptic partial differential
equations of second order, 2nd ed., Grundlehren der Mathematischen
Wissenschaften No. 224, Springer-Verlag, Berlin-New York (1983).
[18] E. Hopf, Remark on a preceding paper of D. Gilbarg, J. Rat. Mech.
Anal. 1 (1952), 419-424.
[19] S. Koike, A beginner’s guide to the theory of viscosity
solutions, MSJ Memoirs 13, (2004).
[20] S. Koike and T. Takahashi, Remarks on regularity of viscosity
solutions for fully nonlinear uniformly elliptic PDE’s with
measurable ingredients, Adv. Differential Equations 7(4) (2002),
493-512.
[21] V. A. Kondrate’v and E. M. Landis, Qualitative theory of
second order linear partial differential equations, partial
differential equations III, Yu. V. Egorov and M. A. Shubin, eds.,
Encyclopedia of Mathematical Sciences 32 (1991), 87-192.
[22] N. V. Krylov and M. V. Safonov, An estimate on the probability
that a diffusion hits a set of positive measure, Soviet Math. 20
(1979), 253-256.
[23] E. M. Landis, Second order equations of elliptic and parabolic
type, Translations of Mathematical Monographs 171, (1998).
[24] K. Miller, Extremal barriers on cones with
Phragmèn-Lindelöf theorems and other applications, Ann. Mat.
(1971), 297-329.
[25] J. K. Oddson, Phragmèn-Lindelöf theorems for elliptic
equations in the plane, Trans. Amer. Math. Soc. 145 (1969),
347-356.
[26] M. H. Protter and H. F. Weinberger, Maximum Principles in
Differential Equations, 2nd ed., Springer Berlin, 1984.
[27] N. S. Trudinger, Local estimates for sub solutions and super
solutions of general second order elliptic quasilinear equations, Inv.
Math. 61 (1980), 67-79.
[28] A. Vitolo, On the Phragmèn-Lindelöf principle for
second-order elliptic equations, Journal of Mathematical Analysis and
Applications 300(1) (2004), 244-259.
[29] A. Vitolo, A note on the maximum principle for complete
second-order elliptic operators in general domains, Acta Math. Sin.
23(11) (2007), 1955-1966.
