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

Emamizadeh, Behrouz; Liu, Yichen

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.

Citation

Emamizadeh, B., & Liu, Y. (2015). Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator. Israel Journal of Mathematics, 206(1), https://doi.org/10.1007/s11856-014-1141-9

• Journal Article Type: Article
• Acceptance Date: Feb 9, 2014
• Online Publication Date: Dec 16, 2014
• Publication Date: Feb 28, 2015
• Deposit Date: Apr 18, 2018
• Publicly Available Date: Apr 18, 2018
• Journal: Israel Journal of Mathematics
• Print ISSN: 0021-2172
• Electronic ISSN: 1565-8511
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 206
• Issue: 1
• DOI: https://doi.org/10.1007/s11856-014-1141-9
• Keywords: Minimization, Rearrangement theory, Existence, Uniqueness, Radial solutions, subdifferentials
• Public URL: https://nottingham-repository.worktribe.com/output/744185
• Publisher URL: https://doi.org/10.1007/s11856-014-1141-9
• 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
• Contract Date: Apr 18, 2018