Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator

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Emamizadeh, Behrouz and Liu, Yichen (2015) Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator. Israel Journal of Mathematics, 206 (1). pp. 281-298. ISSN 0021-2172

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Abstract

In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem

−∆pu = f in D, u = 0 on ∂D.

In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also consider the case when D is a planar disk and show that the minimizer is radial and increasing. In the constrained problem we minimize the energy functional relative to the intersection of a rearrangement class with an affine subspace of codimension one in an appropriate function space. We briefly discuss our motivation for studying the constrained minimization problem.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/744185
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-014-1141-9
Keywords: Minimization, Rearrangement theory, Existence, Uniqueness, Radial solutions, subdifferentials
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering
Identification Number: https://doi.org/10.1007/s11856-014-1141-9
Depositing User: LI, Zhilin
Date Deposited: 18 Apr 2018 08:29
Last Modified: 04 May 2020 17:01
URI: https://eprints.nottingham.ac.uk/id/eprint/50884

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