@article{ASNSP_1997_4_24_3_537_0, author = {Nadirashvili, Nikolai}, title = {Nonuniqueness in the martingale problem and the {Dirichlet} problem for uniformly elliptic operators}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {537--550}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 24}, number = {3}, year = {1997}, mrnumber = {1612401}, zbl = {0907.35039}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_1997_4_24_3_537_0/} }
TY - JOUR AU - Nadirashvili, Nikolai TI - Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 SP - 537 EP - 550 VL - 24 IS - 3 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_1997_4_24_3_537_0/ LA - en ID - ASNSP_1997_4_24_3_537_0 ER -
%0 Journal Article %A Nadirashvili, Nikolai %T Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1997 %P 537-550 %V 24 %N 3 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_1997_4_24_3_537_0/ %G en %F ASNSP_1997_4_24_3_537_0
Nadirashvili, Nikolai. Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 3, pp. 537-550. http://archive.numdam.org/item/ASNSP_1997_4_24_3_537_0/
[A] Uniqueness conditions and estimates for the solutions of the Dirichlet problem, Vestnik Leningrad Univ. Math. 18 (1963), 5-29, Russian; English translation Amer. Math. Soc. Trans. 68 (1968), 89-119. | MR | Zbl
,[A-M] A class of elliptic operators in R 3 in non-divergence form with measurable coefficients, Matematiche 48 (1993), 163-177. | MR | Zbl
- ,[A-T] Second order elliptic equations whose coefficients have their first derivatives weakly Ln, Annali Mat. Pura Appl. 38 (331-340), 1984. | MR | Zbl
- ,[B-P] Uniqueness for diffusion with piecewise constant coefficients, Probab. Theory Related Fields 76 (1987), 557-572. | MR | Zbl
- ,[B-L-P] Asymptotic Analysis for Periodic Structures, North-Holland, 1978. | MR | Zbl
- - ,[B-J-S] Partial differential equations, J.Wiley & S. New York, 1964. | MR | Zbl
, , ,[C-E-F1] Uniquiness for some diffusion with discontinuous coefficients, Ann. Probab. 19 (1991), 525-537. | MR | Zbl
- - ,[C-E-F2] Uniquiness in the Dirichlet problem for some elliptic operators with discontinuous coefficients, Ann. Mat. Pura Appl. 16 (1993), 161-180. | MR | Zbl
- , ,[C] Zero order a priori estimates for solutions of elliptic differential equations, Pros. Sympos. Pure Math. 4 Providence RI, 1961. | MR | Zbl
,[F] Dirichlet's problem for an equation with periodic coefficients depending on a small parameter, Theory Probab. Appl. 9 (1964), 121-125. | MR | Zbl
,[G-S] On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4 (1955/1956), 309-340. | MR | Zbl
- ,[G-T] Elliptic partial differential equations of second order, 2nd ed., Springer, New York, 1983. | MR | Zbl
- ,[K1] On Itô's stochastic integral equations, Theory Probab. Appl.14 (1969), 330-336. | MR | Zbl
,[K2] Once more about connection between elliptic operators and Itô's stochastic equations, In: Statistics and Control of Stoch. Proc., Optimiz. Software, New York, 1985, pagg. 214-229. | MR | Zbl
,[K3] One-point uniqueness for elliptic equations, Comm. Partial Differential Equations. 17 (1992), 1759-1784. | MR | Zbl
,[K-S] A certain property of solutions of parabolic equations with measurable coefficients, Math USSR Izv. 16 (1981), 151-164. | Zbl
- ,[L1] Problems, In: Some unsolved problems in the theory of differential equations and mathematical physics, Russ. Math. Surv. 44 (1989), 157-171. | MR
,[L2] Theorems on the uniqueness of solutions to the Dirichlet problem for elliptic second order equations, Russian, Trudy Moscov. Mat. Obshch. 42 (1981), 50-63. | MR | Zbl
,[L] Une inégalité pour les opérateurs elliptiques du second ordere, Ann. Mat. Pura Appl. 127 (1981), 1-11. | MR | Zbl
,[M-P] Nonhomogenuous Dirichlet problem for elliptic oprators with axially discontinuous coefficients, J. Differential Equations 55 (1984), 368-384. | MR | Zbl
- ,[N] Some differentiability properties of solutions of elliptic equations with measurable coeffitients, Math. USSR-Izv. 27 (1986), 601-606. | Zbl
,[P] Limitazioni per soluzioni di equazioni ellitiche, Ann. Mat. Pura Appl. 74 (1966), 15-30. | MR | Zbl
,[P-T] Elliptic (second order) partial differential equations with measurable coefficients and approximating integral equations, Adv. Math. 19 (1976), 48-105. | MR
- ,[S1] Uniprovability of estimates of Holder constants for solutions of linear elliptic equations with measurable coefficients, Math. USSR Sb. 60 (1988), 269-281. | MR | Zbl
,[S2] On a weak uniqueness for some elliptic equations, Comm. Partial Differential. Equations. 19 5-6 (1994), 959-1014. | MR | Zbl
,[S-V] Multidimentional Diffusion Processes, Springer, New York, 1979. | Zbl
, ,[T] Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl. 69 (1965), 285-304. | MR | Zbl
,