Positive difference operators on general meshes

Duke Mathematical Journal

Volumn 83, Issue 2, 1996, Pages 415-433

  Kuo, Hung Ju ^a   Trudinger, Neil S ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000483302     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-96-08314-3     Document Type: Article

References (16)

1. A. D. ALEKSANDROV, Uniqueness conditions and bounds for the solution of the Dirichlet problem, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom. 18: 3 (1963), 5-29 (in Russian); English translation in Amer. Math. Soc. Transi. Ser. 2 68 (1968), 89-119.
2. A. D. ALEKSANDROV, Uniqueness conditions and bounds for the solution of the Dirichlet problem, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom. 18: 3 (1963), 5-29 (in Russian); English translation in Amer. Math. Soc. Transi. Ser. 2 68 (1968), 89-119.
3. I. YA. BAKEL'MAN, On the theory of quasilinear elliptic equations, Sibirsk. Mat. Zh. 2 (1961), 179-186 (in Russian).
4. D. GILBARG AND N. S. TRUDINGER, Elliptic partial differential equations of second order, 2d ed., Grundlehren Math. Wiss. 224, Springer-Verlag, 1983.
5. M. KOCAN, Approximation of viscosity solutions of elliptic partial differential equations on minimal grids, Numer. Math. 72 (1995), 73-92.
6. N. Y. KRYLOV AND M. V. SAFONOV, A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 161-175 (in Russian); English translation in Math. USSR Izv. 16 (1981), 151-164.
7. N. Y. KRYLOV AND M. V. SAFONOV, A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 161-175 (in Russian); English translation in Math. USSR Izv. 16 (1981), 151-164.
8. H. J. KUO AND N. S. TRUDINGER, Linear elliptic difference inequalities with random coefficients, Math. Comp. 55 (1990), 37-53.
9. _, Discrete methods for fully nonlinear elliptic equations, SIAM J. Numer. Anal. 29 (1992), 123-135.
10. _, On the discrete maximum principle for parabolic difference operators, RAIRO Modél. Math. Anal. Numér. 27 (1993), 719-737.
11. _, Local estimates for parabolic difference operators, J. Differential Equations 122 (1995), 398-413.
12. _, "Maximum principles for difference operators" in Partial Differential Equations and Applications: Collected papers in Honor of Carlo Pucci, Lecture Notes in Pure and Appl. Math. 177, Marcel Dekker, Inc., 1996, 209-219.
13. A. B. MERKOV, Second-order elliptic equations on graphs, Mat. Sb. (N.S.) 127 (1985), 502-518, 559-560 (in Russian); English translation in Math. USSR Sb. 55 (1986), 493-509.
14. A. B. MERKOV, Second-order elliptic equations on graphs, Mat. Sb. (N.S.) 127 (1985), 502-518, 559-560 (in Russian); English translation in Math. USSR Sb. 55 (1986), 493-509.
15. T. MOTZKIN AND W. WASOW, On the approximation of linear elliptic differential equations by difference equations with positive coefficients, J. Math. Phys. 31 (1953), 253-259.
16. N. S. TRUDINGER, Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Invent. Math. 61 (1980), 67-79.