Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics
A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2022-11-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vilniustech.lt/index.php/MMA/article/view/15827 |
| _version_ | 1817975568934633472 |
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| author | Mariana Chivu Cojocaru Andaluzia Matei |
| author_facet | Mariana Chivu Cojocaru Andaluzia Matei |
| author_sort | Mariana Chivu Cojocaru |
| collection | DOAJ |
| description |
A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed.
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| first_indexed | 2024-04-13T21:51:39Z |
| format | Article |
| id | doaj.art-3f7b8529aa7647c1a5952dbc65dd3972 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-13T21:51:39Z |
| publishDate | 2022-11-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-3f7b8529aa7647c1a5952dbc65dd39722022-12-22T02:28:24ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102022-11-0127410.3846/mma.2022.15827Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physicsMariana Chivu Cojocaru0Andaluzia Matei1Doctoral School of Sciences, University of Craiova, A.I. Cuza 13, 200585 Craiova, RomaniaDepartment of Mathematics, University of Craiova, A.I. Cuza 13, 200585 Craiova, Romania A new variational approach for a boundary value problem in mathematical physics is proposed. By considering two-field Lagrange multipliers, we deliver a variational formulation consisting of a mixed variational problem which is equivalent with a saddle point problem. Thus, the unique solvability of the weak formulation we propose is governed by the saddle point theory. Alternative variational formulations and some of their connections are also discussed. https://journals.vilniustech.lt/index.php/MMA/article/view/15827partial differential equationssubdifferential inclusionstwo-field Lagrange multipliersweak solutionssaddle points |
| spellingShingle | Mariana Chivu Cojocaru Andaluzia Matei Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics Mathematical Modelling and Analysis partial differential equations subdifferential inclusions two-field Lagrange multipliers weak solutions saddle points |
| title | Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics |
| title_full | Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics |
| title_fullStr | Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics |
| title_full_unstemmed | Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics |
| title_short | Weak solutions via two-field Lagrange multipliers for boundary value problems in mathematical physics |
| title_sort | weak solutions via two field lagrange multipliers for boundary value problems in mathematical physics |
| topic | partial differential equations subdifferential inclusions two-field Lagrange multipliers weak solutions saddle points |
| url | https://journals.vilniustech.lt/index.php/MMA/article/view/15827 |
| work_keys_str_mv | AT marianachivucojocaru weaksolutionsviatwofieldlagrangemultipliersforboundaryvalueproblemsinmathematicalphysics AT andaluziamatei weaksolutionsviatwofieldlagrangemultipliersforboundaryvalueproblemsinmathematicalphysics |