## Abstract

In [Codres, H.O., 1956, Über die Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen. Mathematische Annalen, 131, 278–312.], Cordes mainly gave some a priori estimates of classical solutions of the Dirichlet problem for quasilinear elliptic equations of second order (Formula presented.) §Dedicated to Professor Wei Lin on the occasion of his 70th birthday. In [Alkhutov, Yu.A. and Mamedov, I.T., 1988, The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients. Mathematical USSR Sbornik, 59, 471–495.] Alkhutov and Mamedov discussed the solvability of the Dirichlet problem for the linear uniformly parabolic equation with measurable coefficients: (Formula presented.) where the coefficients satisfy the conditions: (Formula presented.) In the present article, we try to give estimates of solutions of some boundary value problems, mainly oblique derivative problems for nonlinear uniformly elliptic equations of second order with measurable coefficients in high-dimensional domains, and then prove the solvability of the problems.

Original language | English |
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Pages (from-to) | 1011-1023 |

Number of pages | 13 |

Journal | International Journal of Phytoremediation |

Volume | 85 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2006 |

Externally published | Yes |

## Keywords

- 35J45
- 35J55
- AMS No: 35J65
- Boundary value problems
- High-dimensional domains
- Measurable coefficients
- Nonlinear elliptic equations