Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator
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 con...
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| Format: | Article |
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The Hebrew University Magnes Press
2015
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| Online Access: | https://eprints.nottingham.ac.uk/50884/ |
| _version_ | 1848798361905266688 |
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| author | Emamizadeh, Behrouz Liu, Yichen |
| author_facet | Emamizadeh, Behrouz Liu, Yichen |
| author_sort | Emamizadeh, Behrouz |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:18:33Z |
| format | Article |
| id | nottingham-50884 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:18:33Z |
| publishDate | 2015 |
| publisher | The Hebrew University Magnes Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-508842020-05-04T17:01:52Z https://eprints.nottingham.ac.uk/50884/ Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator Emamizadeh, Behrouz Liu, Yichen 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. The Hebrew University Magnes Press 2015-02-28 Article PeerReviewed 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 Minimization Rearrangement theory Existence Uniqueness Radial solutions subdifferentials https://doi.org/10.1007/s11856-014-1141-9 doi:10.1007/s11856-014-1141-9 doi:10.1007/s11856-014-1141-9 |
| spellingShingle | Minimization Rearrangement theory Existence Uniqueness Radial solutions subdifferentials Emamizadeh, Behrouz Liu, Yichen Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title | Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title_full | Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title_fullStr | Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title_full_unstemmed | Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title_short | Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator |
| title_sort | constrained and unconstrained rearrangement minimization problems related to the p-laplace operator |
| topic | Minimization Rearrangement theory Existence Uniqueness Radial solutions subdifferentials |
| url | https://eprints.nottingham.ac.uk/50884/ https://eprints.nottingham.ac.uk/50884/ https://eprints.nottingham.ac.uk/50884/ |