| dc.contributor.advisor | Schwarzacher, Sebastian | |
| dc.creator | Ferková, Terézia | |
| dc.date.accessioned | 2023-11-06T12:27:27Z | |
| dc.date.available | 2023-11-06T12:27:27Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.11956/184598 | |
| dc.description.abstract | This thesis deals with the one-phase Bernoulli problem, focusing on the existence and regularity of its solutions. After establishing the necessary preliminary theory on function spaces and convergence in the first chapter, we introduce the one-phase Bernoulli problem in the second chapter, reformulating it as a minimization problem. Then, in the third chapter, we present two illuminating examples of solutions to the problem, which imply that the Lipschitz regularity is optimal. The fourth chapter proves the existence of solutions, employing the direct method of calculus of variations. Finally, the fifth chapter reveals the Lipschitz property of generalized solutions. 1 | en_US |
| dc.language | English | cs_CZ |
| dc.language.iso | en_US | |
| dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
| dc.subject | elliptic partial differential equations|calculus of variations|free boundary problems | cs_CZ |
| dc.subject | elliptic partial differential equations|calculus of variations|free boundary problems | en_US |
| dc.title | Free boundary problems | en_US |
| dc.type | bakalářská práce | cs_CZ |
| dcterms.created | 2023 | |
| dcterms.dateAccepted | 2023-09-08 | |
| dc.description.department | Katedra matematické analýzy | cs_CZ |
| dc.description.department | Department of Mathematical Analysis | en_US |
| dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
| dc.description.faculty | Faculty of Mathematics and Physics | en_US |
| dc.identifier.repId | 233056 | |
| dc.title.translated | Problémy s volnou hranicí | cs_CZ |
| dc.contributor.referee | Kampschulte, Malte Laurens | |
| thesis.degree.name | Bc. | |
| thesis.degree.level | bakalářské | cs_CZ |
| thesis.degree.discipline | Obecná matematika | cs_CZ |
| thesis.degree.discipline | General Mathematics | en_US |
| thesis.degree.program | Matematika | cs_CZ |
| thesis.degree.program | Mathematics | en_US |
| uk.thesis.type | bakalářská práce | cs_CZ |
| uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra matematické analýzy | cs_CZ |
| uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Mathematical Analysis | en_US |
| uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
| uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
| uk.faculty-abbr.cs | MFF | cs_CZ |
| uk.degree-discipline.cs | Obecná matematika | cs_CZ |
| uk.degree-discipline.en | General Mathematics | en_US |
| uk.degree-program.cs | Matematika | cs_CZ |
| uk.degree-program.en | Mathematics | en_US |
| thesis.grade.cs | Velmi dobře | cs_CZ |
| thesis.grade.en | Very good | en_US |
| uk.abstract.en | This thesis deals with the one-phase Bernoulli problem, focusing on the existence and regularity of its solutions. After establishing the necessary preliminary theory on function spaces and convergence in the first chapter, we introduce the one-phase Bernoulli problem in the second chapter, reformulating it as a minimization problem. Then, in the third chapter, we present two illuminating examples of solutions to the problem, which imply that the Lipschitz regularity is optimal. The fourth chapter proves the existence of solutions, employing the direct method of calculus of variations. Finally, the fifth chapter reveals the Lipschitz property of generalized solutions. 1 | en_US |
| uk.file-availability | V | |
| uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra matematické analýzy | cs_CZ |
| thesis.grade.code | 2 | |
| uk.publication-place | Praha | cs_CZ |
| uk.thesis.defenceStatus | O | |
