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ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 720864, 10 pages
A Comparison Principle for Some Types of Elliptic Equations
Dipartimento di Matematica, Università degli Studi di Salerno, Via Ponte don Melillo,
84084 Fisciano, Italy
Received 21 July 2012; Accepted 23 October 2012
Academic Editors: B. Djafari-Rouhani, X. B. Pan, and G. Schimperna
Copyright © 2012 Maria Emilia Amendola. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. C. Evans, “Classical solutions of fully nonlinear, convex, second-order elliptic equations,” Communications on Pure and Applied Mathematics, vol. 35, no. 3, pp. 333–363, 1982.
- D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 2nd edition, 1983.
- R. Jensen, “The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations,” Archive for Rational Mechanics and Analysis, vol. 101, no. 1, pp. 1–27, 1988.
- N. S. Trudinger, “Comparison principles and pointwise estimates for viscosity solutions of nonlinear elliptic equations,” Revista Matemática Iberoamericana, vol. 4, no. 3-4, pp. 453–468, 1988.
- R. Jensen, P.-L. Lions, and P. E. Souganidis, “A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations,” Proceedings of the American Mathematical Society, vol. 102, no. 4, pp. 975–978, 1988.
- H. Ishii, “On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs,” Communications on Pure and Applied Mathematics, vol. 42, no. 1, pp. 15–45, 1989.
- H. Ishii and P.-L. Lions, “Viscosity solutions of fully nonlinear second-order elliptic partial differential equations,” Journal of Differential Equations, vol. 83, no. 1, pp. 26–78, 1990.
- M. G. Crandall, “Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 6, no. 6, pp. 419–435, 1989.
- M. G. Crandall and H. Ishii, “The maximum principle for semicontinuous functions,” Differential and Integral Equations, vol. 3, no. 6, pp. 1001–1014, 1990.
- M. G. Crandall, H. Ishii, and P.-L. Lions, “User's guide to viscosity solutions of second order partial differential equations,” Bulletin of the American Mathematical Society, vol. 27, no. 1, pp. 1–67, 1992.
- B. Kawohl and N. Kutev, “Comparison principle and Lipschitz regularity for viscosity solutions of some classes of nonlinear partial differential equations,” Funkcialaj Ekvacioj, vol. 43, no. 2, pp. 241–253, 2000.
- B. Kawohl and N. Kutev, “Strong maximum principle for semicontinuous viscosity solutions of nonlinear partial differential equations,” Archiv der Mathematik, vol. 70, no. 6, pp. 470–478, 1998.
- S. Koike and T. Takahashi, “Remarks on regularity of viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients,” Advances in Differential Equations, vol. 7, no. 4, pp. 493–512, 2002.
- M. Bardi and P. Mannucci, “On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations,” Communications on Pure and Applied Analysis, vol. 5, no. 4, pp. 709–731, 2006.
- M. Bardi and P. Mannucci, “Comparison Principles and Dirichlet problem for fully nonlinear degenerate equations of Monge-Ampere type,” To Appear in Forum Mathematicum.
- B. Sirakov, “Solvability of uniformly elliptic fully nonlinear PDE,” Archive for Rational Mechanics and Analysis, vol. 195, no. 2, pp. 579–607, 2010.
- I. Birindelli and F. Demengel, “Comparison principle and Liouville type results for singular fully nonlinear operators,” Annales de la Faculté des Sciences de Toulouse, vol. 13, no. 2, pp. 261–287, 2004.
- I. Birindelli and F. Demengel, “First eigenvalue and maximum principle for fully nonlinear singular operators,” Advances in Differential Equations, vol. 11, no. 1, pp. 91–119, 2006.
- I. Birindelli and F. Demengel, “Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators,” Communications on Pure and Applied Analysis, vol. 6, no. 2, pp. 335–366, 2007.
- L. A. Caffarelli and X. Cabré, Fully Nonlinear Elliptic Equations, vol. 43 of American Mathematical Society Colloquium Publications, American Mathematical Society, 1995.