Taiwanese Journal of Mathematics

MAXIMIZATION AND MINIMIZATION PROBLEMS RELATED TO A $p$-LAPLACIAN EQUATION ON A MULTIPLY CONNECTED DOMAIN

N. Amiri and M. Zivari-Rezapour

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Abstract

In this paper we investigate maximization and minimization problems related to a $p$-Laplacian equation on a multiply connected domain in $\mathbb{R}^2$, where the admissible set is a rearrangement class of a fixed function. We prove existence and representation of the maximizers and existence, uniqueness and representation of the minimizer.

Article information

Source
Taiwanese J. Math., Volume 19, Number 1 (2015), 243-252.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133628

Digital Object Identifier
doi:10.11650/tjm.19.2015.3873

Mathematical Reviews number (MathSciNet)
MR3313415

Zentralblatt MATH identifier
1357.35166

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 49J20: Optimal control problems involving partial differential equations

Keywords
rearrangement maximization minimization existence uniqueness

Citation

Amiri, N.; Zivari-Rezapour, M. MAXIMIZATION AND MINIMIZATION PROBLEMS RELATED TO A $p$-LAPLACIAN EQUATION ON A MULTIPLY CONNECTED DOMAIN. Taiwanese J. Math. 19 (2015), no. 1, 243--252. doi:10.11650/tjm.19.2015.3873. https://projecteuclid.org/euclid.twjm/1499133628


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