## Tokyo Journal of Mathematics

### A Degenerate Neumann Problem for Quasilinear Elliptic Equations

#### Abstract

The degenerate Neumann problem $\begin{cases} \ \displaystyle \sum_{i,j=1}^{n}a^{ij}(x)\frac{\partial^{2}u}{\partial x_i\partial x_j}=f(x,u,Du) & \text{in}\ \Omega ,\\ \ a(x)\dfrac{\partial u}{\partial v}+b(x)u=\varphi(x) & \text{on}\ \Gamma \end{cases}$ is studied in the case where $a(x)$ and $b(x)$ are non-negative functions on $\Gamma$ such that $a(x)+b(x)>0$ on $\Gamma$. A classical existence and uniqueness theorem in the Hölder space $C^{2+\alpha}(\bar{\Omega})$ is proved under suitable regularity and structure conditions on the data.

#### Article information

Source
Tokyo J. Math., Volume 23, Number 1 (2000), 227-234.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.tjm/1255958817

Digital Object Identifier
doi:10.3836/tjm/1255958817

Mathematical Reviews number (MathSciNet)
MR1763514

Zentralblatt MATH identifier
0960.35043

#### Citation

TAIRA, Kazuaki; PALAGACHEV, Dian K.; POPIVANOV, Peter R. A Degenerate Neumann Problem for Quasilinear Elliptic Equations. Tokyo J. Math. 23 (2000), no. 1, 227--234. doi:10.3836/tjm/1255958817. https://projecteuclid.org/euclid.tjm/1255958817