Linear and fully nonlinear elliptic equations with L_d-drift

References

• Kang, B., Kim, H. (2019). On Lp-resolvent estimates for second-order elliptic equations in divergence form. Potential Anal. 50(1):107–133. DOI: 10.1007/s11118-017-9675-1.
   Web of Science ®Google Scholar
• Caffarelli, L. A. (1989). Interior a priori estimates for solutions of fully non-linear equations. Ann. Math. 130(1):189–213. DOI: 10.2307/1971480.
   Web of Science ®Google Scholar
• Caffarelli, L. A., Cabré, X. (1995). Fully Nonlinear Elliptic Equations. Providence: American Mathematical Society.
   Google Scholar
• Krylov, N. V., Safonov, M. V. (1981). A certain property of solutions of parabolic equations with measurable coefficients, Izvestiya Akademii Nauk SSSR, seriya matematicheskaya, Vol. 44 (1980), No. 1, 161–175 in Russian; English translation in Math. Math. USSR. Izv. 16(1):151–164. DOI: 10.1070/IM1981v016n01ABEH001283.
   Web of Science ®Google Scholar
• Safonov, M. V. (1983). Harnack inequalities for elliptic equations and Hölder continuity of their solutions, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), Vol. 96 (1980), 272–287 in Russian; English translation in. J. Math. Sci. 21(5):851–863. DOI: 10.1007/BF01094448.
   Google Scholar
• Krylov, N. V. (2013). On the existence of Wp2 solutions for fully nonlinear elliptic equations under relaxed convexity assumptions. Commun. Part. Diff. Eq. 38(4):687–710. DOI: 10.1080/03605302.2012.741177.
   Web of Science ®Google Scholar
• Krylov, N. V. (2018). Sobolev and viscosity solutions for fully nonlinear elliptic and parabolic equations. In: Mathematical Surveys and Monographs, Vol. 233. Providence, RI: American Mathematical Society.
   Google Scholar
• Krylov, N. V. On stochastic equations with drift in Ld. Available at: http://arxiv.org/abs/2001.04008
   Google Scholar
• Krylov, N. V. On diffusion processes with drift in Ld. Available at: http://arxiv.org/abs/2001.04950
   Google Scholar
• Escauriaza, L. (1993). W2,n a priori estimates for solutions to fully non-linear equations. Indiana Univ. Math. J. 42(2):413–423. DOI: 10.1512/iumj.1993.42.42019.
   Web of Science ®Google Scholar
• Streets, J., Warren, M. (2016). Evans-Krylov estimates for a nonconvex Monge-Ampère equation. Math. Ann. 365(1–2):805–834. DOI: 10.1007/s00208-015-1293-x.
   Web of Science ®Google Scholar
• Caffarelli, L. A. (1990). Interior W2,p estimates for solutions of the Monge-Ampère equation. Ann. Math. 131(1):135–150. DOI: 10.2307/1971510.
   Web of Science ®Google Scholar
• Caffarelli, L., Crandall, M. G., Kocan, M., Święch, A. (1996). On viscosity solutions of fully nonlinear equations with measurable ingredients. Commun. Pure Appl. Math. 49(4):365–397. DOI: 10.1002/(SICI)1097-0312(199604)49:4<365::AID-CPA3>3.0.CO;2-A.
   Web of Science ®Google Scholar
• Winter, N. (2009). W2,p and W1,p-estimates at the boundary for solutions of fully nonlinear, uniformly elliptic equations. Z. Anal. Anwend. 28(2):129–164.
   Web of Science ®Google Scholar
• Byun, S. S., Lee, M., Palagachev, D. K. (2016). Hessian estimates in weighted Lebesgue spaces for fully nonlinear elliptic equations. J. Differ. Equ. 260(5):4550–4571. DOI: 10.1016/j.jde.2015.11.025.
   Web of Science ®Google Scholar
• Huang, Q. (2019). Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity. Ann. Inst. H. Poincaré, Anal. Non Linéaire. 36(7):1869–1902. DOI: 10.1016/j.anihpc.2019.06.001.
   Web of Science ®Google Scholar
• Pimentel, E., Teixeira, E. (2016). Sharp Hessian integrability estimates for nonlinear equations: An asymptotic approach. J. Math. Pures Appl. 106(4):744–767. DOI: 10.1016/j.matpur.2016.03.010.
   Web of Science ®Google Scholar
• Świȩch, A. (1997). W1,p-interior estimates for solution of fully nonlinear, uniformly elliptic equations. Adv. Differential Equ. 2(6):1005–1027.
   Google Scholar
• Fok, K. (1998). A nonlinear Fabes-Stroock result. Commun. PDEs. 23(5–6):967–983. DOI: 10.1080/03605309808821375.
   Web of Science ®Google Scholar
• Koike, S., Święch, A. (2009). Existence of strong solutions of Pucci extremal equation with superlinear growth in Du. J. Fixed Point Theory Appl. 5(2):291–304. DOI: 10.1007/s11784-009-0106-9.
   Web of Science ®Google Scholar
• Koike, S., Święch, A. (2009). Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients. J. Math. Soc. Jpn. 61(3):723–755. DOI: 10.2969/jmsj/06130723.
   Web of Science ®Google Scholar
• Koike, S., Świech, A. (2012). Local maximum principle for Lp-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Commun. Pure Appl. Anal. 11(5):1897–1910. DOI: 10.3934/cpaa.2012.11.1897.
   Web of Science ®Google Scholar
• Nagakawa, K. (2009). Maximum principle for Lp-viscosity solutions of fully nonlinear equations with unbounded ingredients and superlinear growth term. Adv. Math. Sci. Appl. 19(1):89–107.
   Google Scholar
• Nornberg, G. (2019). C1,α regularity for fully nonlinear elliptic equations with superlinear growth in the gradient. J. Math. Pures Appl. 128(9):297–329. DOI: 10.1016/j.matpur.2019.06.008.
   Web of Science ®Google Scholar
• Sirakov, B. (2010). Solvability of uniformly elliptic fully nonlinear PDE. Arch. Rational Mech. Anal. 195(2):579–607. DOI: 10.1007/s00205-009-0218-9.
   Web of Science ®Google Scholar
• Safonov, M. V. (2010). Non-divergence elliptic equations of second order with unbounded drift, Nonlinear partial differential equations and related topics, 211–232, Amer. Math. Soc. Transl. Ser. 2, 229. Providence, RI: American Mathematical Society.
   Google Scholar
• Ladyzhenskaya, O. A., Ural'tseva, N. N. (1987). Estimates of the Hölder constant for functions satisfying a uniformly elliptic or a uniformly parabolic quasilinear inequality with unbounded coefficients, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI), Vol. 147 (1985), 72–94 (in Russian). English transl. in. J. Soviet Math. 37(1):837–851. DOI: 10.1007/BF01387722.
   Google Scholar
• Safonov, M. V. (1989). On the classical solutions of nonlinear elliptic equations of second order, Izvestija Acad. Nauk SSSR, ser. matemat., Vol. 52 (1988), No. 6, 1272–1287 in Russian. Math. USSR. Izv. 33(3):597–612. DOI: 10.1070/IM1989v033n03ABEH000858.
   Google Scholar
• Cabré, X. (1995). On the Alexandroff-Bakelman-Pucci estimate and the reversed Hölder inequality for solutions of elliptic and parabolic equations. Commun. Pure Appl. Math. 48(5):539–570. DOI: 10.1002/cpa.3160480504.
   Web of Science ®Google Scholar
• Safonov, M. V. (1984). On the classical solutions of Bellman’s elliptic equations, Dokl. Akad. Nauk SSSR, Vol. 278 (1984), 810–813 in Russian. Soviet Math. Dokl. 30(2):482–485.
   Google Scholar
• Krylov, N. V. (1987). Nonlinear Elliptic and Parabolic Equations of Second Order (1985 in Russian; English translation). Nauka, Moscow Dordrecht: Reidel.
   Google Scholar
• Krylov, N. V. (1971). On uniqueness of the solution of Bellman’s equation, Izvestiya Akademii Nauk SSSR, seriya matematicheskaya, Vol. 35 (1971), No. 6, 1377–1388 in Russian. Math. USSR. Izv. 5(6):1387–1398. DOI: 10.1070/IM1971v005n06ABEH001259.
   Google Scholar
• Evans, L. C. (1978). A convergence theorem for solutions of nonlinear second order elliptic equations. Indiana Univ. Math. J. 27(5):875–887. DOI: 10.1512/iumj.1978.27.27059.
   Web of Science ®Google Scholar