Optimization problems with fixed volume constraints and stability results related to rearrangement classes
The material in this paper has been divided into two main parts. In the first part we describe two optimization problems—one maximization and one minimization—related to a sharp trace inequality that was recently ob- tained by G. Auchmuty. In both problems the admissible set is the one comprising ch...
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/50886/ |
| _version_ | 1848798362182090752 |
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| author | Liu, Yichen Emamizadeh, Behrouz Farjudian, Amin |
| author_facet | Liu, Yichen Emamizadeh, Behrouz Farjudian, Amin |
| author_sort | Liu, Yichen |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The material in this paper has been divided into two main parts. In the first part we describe two optimization problems—one maximization and one minimization—related to a sharp trace inequality that was recently ob- tained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure. We prove the maximization to be solvable, whilst the minimization will turn out not to be solvable in general. We will also discuss the case of radial do- mains. In the second part of the paper, we study approximation and stability results regarding rearrangement optimization problems. First, we show that if a sequence of the generators of rearrangement classes converges, then the corresponding sequence of the optimal solutions will also converge. Second, a stability result regarding the Hausdorff distance between the weak closures of two rearrangement classes is presented. |
| first_indexed | 2025-11-14T20:18:34Z |
| format | Article |
| id | nottingham-50886 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:18:34Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-508862020-05-04T18:21:03Z https://eprints.nottingham.ac.uk/50886/ Optimization problems with fixed volume constraints and stability results related to rearrangement classes Liu, Yichen Emamizadeh, Behrouz Farjudian, Amin The material in this paper has been divided into two main parts. In the first part we describe two optimization problems—one maximization and one minimization—related to a sharp trace inequality that was recently ob- tained by G. Auchmuty. In both problems the admissible set is the one comprising characteristic functions whose supports have a fixed measure. We prove the maximization to be solvable, whilst the minimization will turn out not to be solvable in general. We will also discuss the case of radial do- mains. In the second part of the paper, we study approximation and stability results regarding rearrangement optimization problems. First, we show that if a sequence of the generators of rearrangement classes converges, then the corresponding sequence of the optimal solutions will also converge. Second, a stability result regarding the Hausdorff distance between the weak closures of two rearrangement classes is presented. Elsevier 2016-11-15 Article PeerReviewed Liu, Yichen, Emamizadeh, Behrouz and Farjudian, Amin (2016) Optimization problems with fixed volume constraints and stability results related to rearrangement classes. Journal of Mathematical Analysis and Applications, 443 (2). pp. 1293-1310. ISSN 0022-247X Trace inequality Boundary value problem Maximization Mini- mization Approximation Stability Rearrangement theory https://www.sciencedirect.com/science/article/pii/S0022247X16302475?via%3Dihub doi:10.1016/j.jmaa.2016.06.017 doi:10.1016/j.jmaa.2016.06.017 |
| spellingShingle | Trace inequality Boundary value problem Maximization Mini- mization Approximation Stability Rearrangement theory Liu, Yichen Emamizadeh, Behrouz Farjudian, Amin Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title | Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title_full | Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title_fullStr | Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title_full_unstemmed | Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title_short | Optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| title_sort | optimization problems with fixed volume constraints and stability results related to rearrangement classes |
| topic | Trace inequality Boundary value problem Maximization Mini- mization Approximation Stability Rearrangement theory |
| url | https://eprints.nottingham.ac.uk/50886/ https://eprints.nottingham.ac.uk/50886/ https://eprints.nottingham.ac.uk/50886/ |