Differential and Integral Equations

Comparison results for solutions of elliptic problems via Steiner symmetrization

F. Chiacchio and V. M. Monetti

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations, Volume 14, Number 11 (2001), 1351-1366.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123028

Mathematical Reviews number (MathSciNet)
MR1859610

Zentralblatt MATH identifier
1027.35026

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35A30: Geometric theory, characteristics, transformations [See also 58J70, 58J72] 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Citation

Chiacchio, F.; Monetti, V. M. Comparison results for solutions of elliptic problems via Steiner symmetrization. Differential Integral Equations 14 (2001), no. 11, 1351--1366. https://projecteuclid.org/euclid.die/1356123028


Export citation