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2001 Comparison results for solutions of elliptic problems via Steiner symmetrization
F. Chiacchio, V. M. Monetti
Differential Integral Equations 14(11): 1351-1366 (2001).

Abstract

We consider the Dirichlet problem for a class of linear elliptic equations, whose model is \begin{align*} & -\Delta u-\sum _{i=1}^{n}\left( b_{i}(y)u\right) _{x_{i}}-\sum _{j=1}^{m}\left( \widetilde{b}_{j}(y)u\right) _{y_{j}}+ \sum _{i=1}^{n}d_{i}(y)u_{x_{i}} \\ & +\sum\limits_{j=1}^{m}\widetilde{d} _{j}(y)u_{y_{j}}+c(y)u=f(x,y) \ \ \text{ in }G, \end{align*} where $G=G^{\prime }\times G^{\prime \prime }$ is an open, bounded and connected subset of ${\mathbb R}^{N}={\mathbb R}^{n}\times {\mathbb R}^{m}$, the coefficients $b_{i}(y),$ $\widetilde{b}_{j}(y),$ $d_{i}(y)$, $\widetilde{d} _{j}(y)$ and $c(y)$ are in $L^{\infty }(G)$ and the datum $f(x,y)$ belongs to $ L^{p}(G)$ with $p>\frac{N}{2}$. We prove some comparison results by using Steiner symmetrization.

Citation

Download Citation

F. Chiacchio. V. M. Monetti. "Comparison results for solutions of elliptic problems via Steiner symmetrization." Differential Integral Equations 14 (11) 1351 - 1366, 2001.

Information

Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1027.35026
MathSciNet: MR1859610

Subjects:
Primary: 35J25
Secondary: 35A30, 35B05

Rights: Copyright © 2001 Khayyam Publishing, Inc.

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Vol.14 • No. 11 • 2001
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