Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 3, pp. 537-550. 
@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, Série 4, Tome 24 (1997) no. 3, pp. 537-550. http://archive.numdam.org/item/ASNSP_1997_4_24_3_537_0/

[A] A.D. Alexandrov, 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] O. Arena - P. Manselli, A class of elliptic operators in R 3 in non-divergence form with measurable coefficients, Matematiche 48 (1993), 163-177. | MR | Zbl

[A-T] A. Alvino - G. Trombetti, Second order elliptic equations whose coefficients have their first derivatives weakly Ln, Annali Mat. Pura Appl. 38 (331-340), 1984. | MR | Zbl

[B-P] R.F. Bass - E. Padoux, Uniqueness for diffusion with piecewise constant coefficients, Probab. Theory Related Fields 76 (1987), 557-572. | MR | Zbl

[B-L-P] A. Bensoussan - J.L. Lions - G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, 1978. | MR | Zbl

[B-J-S] L. Bers, F. John, M. Schecter, Partial differential equations, J.Wiley & S. New York, 1964. | MR | Zbl

[C-E-F1] M.C. Cerutti - L. Escauriaza - E.B. Fabes, Uniquiness for some diffusion with discontinuous coefficients, Ann. Probab. 19 (1991), 525-537. | MR | Zbl

[C-E-F2] M.C. Cerutti - L. Escauriaza, E.B. Fabes, Uniquiness in the Dirichlet problem for some elliptic operators with discontinuous coefficients, Ann. Mat. Pura Appl. 16 (1993), 161-180. | MR | Zbl

[C] H.O. Cordes, Zero order a priori estimates for solutions of elliptic differential equations, Pros. Sympos. Pure Math. 4 Providence RI, 1961. | MR | Zbl

[F] M.I. Freidlin, 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] D. Gilbarg - J. Serrin, On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math. 4 (1955/1956), 309-340. | MR | Zbl

[G-T] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer, New York, 1983. | MR | Zbl

[K1] N.V. Krylov, On Itô's stochastic integral equations, Theory Probab. Appl.14 (1969), 330-336. | MR | Zbl

[K2] N.V. Krylov, 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] N.V. Krylov, One-point uniqueness for elliptic equations, Comm. Partial Differential Equations. 17 (1992), 1759-1784. | MR | Zbl

[K-S] N.V. Krylov - M.V. Safonov, A certain property of solutions of parabolic equations with measurable coefficients, Math USSR Izv. 16 (1981), 151-164. | Zbl

[L1] E.M. Landis, Problems, In: Some unsolved problems in the theory of differential equations and mathematical physics, Russ. Math. Surv. 44 (1989), 157-171. | MR

[L2] E.M. Landis, 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] P.L. Lions, Une inégalité pour les opérateurs elliptiques du second ordere, Ann. Mat. Pura Appl. 127 (1981), 1-11. | MR | Zbl

[M-P] P. Manselli - G. Papi, Nonhomogenuous Dirichlet problem for elliptic oprators with axially discontinuous coefficients, J. Differential Equations 55 (1984), 368-384. | MR | Zbl

[N] N.S. Nadirashvili, Some differentiability properties of solutions of elliptic equations with measurable coeffitients, Math. USSR-Izv. 27 (1986), 601-606. | Zbl

[P] C. Pucci, Limitazioni per soluzioni di equazioni ellitiche, Ann. Mat. Pura Appl. 74 (1966), 15-30. | MR | Zbl

[P-T] C. Pucci - G. Talenti, Elliptic (second order) partial differential equations with measurable coefficients and approximating integral equations, Adv. Math. 19 (1976), 48-105. | MR

[S1] M.V. Safonov, 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] M.V. Safonov, On a weak uniqueness for some elliptic equations, Comm. Partial Differential. Equations. 19 5-6 (1994), 959-1014. | MR | Zbl

[S-V] D.W. Strook, S.R.S. Varadhan, Multidimentional Diffusion Processes, Springer, New York, 1979. | Zbl

[T] G. Talenti, Sopra una classe di equazioni ellittiche a coefficienti misurabili, Ann. Mat. Pura Appl. 69 (1965), 285-304. | MR | Zbl