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June 2000 A Degenerate Neumann Problem for Quasilinear Elliptic Equations
Dian K. PALAGACHEV, Peter R. POPIVANOV, Kazuaki TAIRA
Tokyo J. Math. 23(1): 227-234 (June 2000). DOI: 10.3836/tjm/1255958817

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.

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Dian K. PALAGACHEV. Peter R. POPIVANOV. Kazuaki TAIRA. "A Degenerate Neumann Problem for Quasilinear Elliptic Equations." Tokyo J. Math. 23 (1) 227 - 234, June 2000. https://doi.org/10.3836/tjm/1255958817

Information

Published: June 2000
First available in Project Euclid: 19 October 2009

zbMATH: 0960.35043
MathSciNet: MR1763514
Digital Object Identifier: 10.3836/tjm/1255958817

Rights: Copyright © 2000 Publication Committee for the Tokyo Journal of Mathematics

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Vol.23 • No. 1 • June 2000
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