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

Emamizadeh, Behrouz; Liu, Yichen

Authors

Behrouz Emamizadeh

Yichen Liu



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 0021-2172
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 http://eprints.nottingham.ac.uk/id/eprint/50884
Publisher URL https://doi.org/10.1007/s11856-014-1141-9
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf



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