Trudinger, Neil S. Hölder gradient estimates for fully nonlinear elliptic equations. (English) Zbl 0653.35026 Proc. R. Soc. Edinb., Sect. A 108, No. 1-2, 57-65 (1988). The author proves Hölder estimates for the gradient of Lipschitz continuous viscosity solutions of fully nonlinear elliptic equations F(x,u,Du,D \(2u)=0\), thereby generalizing some of his earlier results for classical solutions [see the author, Trans. Am. Math. Soc. 278, 751-769 (1983; Zbl 0518.35036)]. As a special case the results are applicable to Isaac’s equation from stochastic game theory \(F\equiv \inf_{\alpha} \sup_{\beta}(L_{\alpha \beta}u-f_{\alpha \beta})\), where \(L_{\alpha \beta}\) is a family of second order linear operators. Reviewer: M.Wiegner Cited in 2 ReviewsCited in 41 Documents MSC: 35J60 Nonlinear elliptic equations 35B45 A priori estimates in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs Keywords:Hölder estimates; viscosity solutions; fully nonlinear; classical solutions; Isaac’s equation; stochastic game theory Citations:Zbl 0518.35036 PDFBibTeX XMLCite \textit{N. S. Trudinger}, Proc. R. Soc. Edinb., Sect. A, Math. 108, No. 1--2, 57--65 (1988; Zbl 0653.35026) Full Text: DOI References: [1] Gilbarg, Elliptic partial differential equations of second order (1983) · Zbl 0562.35001 · doi:10.1007/978-3-642-61798-0 [2] Krylov, Izv. Akad. Nauk SSSR Ser. Mat. 47 pp 75– (1983) [3] Trudinger, Nat. Univ. Centre for Math. Anal. Research Report 45 (1987) [4] DOI: 10.1090/S0002-9939-1985-0796449-X · doi:10.1090/S0002-9939-1985-0796449-X [5] Trudinger, Proc. Centre Math. Anal. Aust. Nat. Univ. 8 pp 65– (1984) [6] DOI: 10.1090/S0002-9947-1983-0701522-0 · doi:10.1090/S0002-9947-1983-0701522-0 [7] DOI: 10.1215/S0012-7094-87-05521-9 · Zbl 0697.35030 · doi:10.1215/S0012-7094-87-05521-9 [8] DOI: 10.1007/BF01389895 · Zbl 0453.35028 · doi:10.1007/BF01389895 [9] DOI: 10.1080/03605308308820301 · Zbl 0716.49023 · doi:10.1080/03605308308820301 [10] DOI: 10.1007/BF01229801 · Zbl 0616.35028 · doi:10.1007/BF01229801 [11] Krylov, Izv. Akad. Nauk. SSSR Ser. Mat. 40 pp 161– (1980) [12] DOI: 10.1080/03605308608820422 · Zbl 0589.35036 · doi:10.1080/03605308608820422 [13] Krylov, Dokl. Akad. Nauk UzSSR 274 pp 21– (1983) [14] Ladyzhenskaya, Linear and quasilinear elliptic equations (1964) · Zbl 0143.33602 [15] Trudinger, Nat. Univ. Centre for Math. Anal. Research Report 46 (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.