Comparison principle and Liouville type results for singular fully nonlinear operators

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1. [1] Berestycki ( H. ), Capuzzo Dolcetta ( I.), Nirenberg ( L.). - Problèmes Elliptiques indéfinis et Théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris Sér. I Math.317, no. 10, p. 945-950 (1993). Zbl0820.35056MR1249366
2. [2] Berestycki ( H.), Capuzzo Dolcetta ( I.), Nirenberg ( L.). - Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal.4, no. 1, p. 59-78 (1994). Zbl0816.35030MR1321809
3. [3] Birindelli ( I.), Demengel ( F.). - Some Liouville Theorems for the p-Laplacian, Elec. J. Differential Equations, Conference 08, 2002. Zbl1034.35031MR1990294
4. [4] Wigniolle ( J. ). - A strong maximum principle for fully non linear degenerate operators, Prépublications de l'université de Cergy-Pontoise. 
5. [5] Birindelli ( I.), Mitidieri ( E.). - Liouville theorems for elliptic inequalities and applications, Proc. Roy. Soc. Edinburgh Sect.A128, no. 6, p. 1217-1247 (1998). Zbl0919.35023MR1664101
6. [6] L. Caffarelli ( L.), Cabré ( X.). - Fully-nonlinear equations, Colloquium Publications43, American Mathematical Society, Providence, RI (1995). Zbl0834.35002
7. [7] Chen ( Y.G. ), Giga ( Y.), Goto ( S.). - Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations , Journal of Differential Geometry33, p. 749-786 (1991). Zbl0696.35087MR1100211
8. [8] Crandall ( M.G.), Ishii ( H.), Lions ( P.L.). - User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.)27, no. 1, p. 1-67 (1992). Zbl0755.35015MR1118699
9. [9] Cutri ( A.) , Leoni ( F.). - On the Liouville property for fully-nonlinear equationsAnnales de l'Institut H. Poincaré, Analyse non-linéaire , p. 219-245 (2000). Zbl0956.35035MR1753094
10. [10] Evans ( C. ), Spruck ( J.). - Motion of level sets by mean curvature, Journal of Diff. Geom.33, p. 635-681 (1991). Zbl0726.53029MR1100206
11. [11] Gidas ( B.). — Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations, Nonlinear Partial Differential equations in engineering and applied sciences, Eds. R. Sternberg, A. Kalinowski and J. Papadakis, Proc. Conf. Kingston, R.I 1979, Lect. Notes on pure appl. maths, 54, Decker, New York, p. 255-273 (1980). Zbl0444.35038MR577096
12. [12] Ishii ( H. ). - Viscosity solutions of non-linear partial differential equations, Sugaku Expositions vol 9, (1996). Zbl0968.35002MR1426875
13. [13] Jensen ( R. ). - The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal.101, p. 1-27 (1988). Zbl0708.35019MR920674
14. [14] Jensen ( R. ), Lions ( P.L.), Souganidis ( T.). - A uniqueness result for viscosity solutions of second order fully-nonlinear partial differential equations, Proc. Amer. Math. Soc.102, p. 975-978 (1988). Zbl0662.35048MR934877
15. [15] Juutinen ( P.), Lindquist ( P.), Manfredi ( J.). - On the equivalence of viscosity solutions and weak solutions for a quasi linear equation, SIAM J. Math. Anal.33, no. 3, p. 699-717 (2001). Zbl0997.35022MR1871417
16. [16] Mitidieri ( E.), Pohozaev ( S.). - Absence of positive solutions for quasilinear elliptic problems in RN, (RussianTr. Mat. Inst. Steklova227 (1999), Issled. po Teor. Differ. Funkts. Mnogikh Perem. i ee Prilozh. 18, p. 192-222; translation in Proc. Steklov Inst. Math.1999, no. 4 (227), p. 186-216. Zbl1056.35507
17. [17] Serrin ( J. ), Zou ( H.). - Cauchy-Liouville and universal boundedness theorems for quasi-linear elliptic equations, Acta Math.189, no. 1, p. 79-142 (2002). Zbl1059.35040MR1946918
18. [18] Vasquez ( J.L.). - A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim.12, p. 191-202, (1984). Zbl0561.35003

1. I. Birindelli, F. Demengel, 𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations