Global regularity of solutions of nonlinear second order elliptic and parabolic differential equations. (English) Zbl 0616.35028
This work considers solutions of Dirichlet problems for a fully nonlinear elliptic equation of second order in a smooth, bounded domain \(\subset\mathbb R^n\). Under certain conditions on the equation and weak smoothness assumptions on the solution local, boundary and global second derivative Hölder estimates are obtained. Parabolic versions of the results are discussed in the final section. The author states that similar results are obtained by N. V. Krylov [Sov. Math., Dokl. 29, 14–17 (1984); translation from Dokl. Akad. Nauk SSSR 274, 23–26 (1984; Zbl 0598.35057)] and M. V. Safonov [ibid. 30, 482-485 (1984); translation from Dokl. Akad. Nauk SSSR 278, 810–813 (1984; Zbl 0595.35011)] providing alternative derivations.
Reviewer: J. Weisel (Lollar-Ruttershausen)
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35K55 | Nonlinear parabolic equations |
References:
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