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Properties of obstacle problem and free boundary problem
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이기암 | - |
| dc.contributor.author | 박진완 | - |
| dc.date.accessioned | 2017-07-19T08:59:58Z | - |
| dc.date.available | 2017-07-19T08:59:58Z | - |
| dc.date.issued | 2014-08 | - |
| dc.identifier.other | 000000021309 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/131485 | - |
| dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2014. 8. 이기암. | - |
| dc.description.abstract | This paper is a paper which is written based on the contents of [1] and introduction of obstacle
problem for nonlinear second-order parabolic operator. In chapter 1, we introduce classical obstacle problem and we deal with existence, uniqueness and C1 | - |
| dc.description.abstract | 1 regularity of solution of the
problem. In chapter 2, we show C1 | - |
| dc.description.abstract | 1 regularity of solution of Obstacle-type problem. In chapter
3, we prove some elementary properties of free boundary. In chapter 4, We reference [2] to show the continuity of solution of obstacle problem for nonlinear second-order parabolic operator. Key | - |
| dc.description.tableofcontents | 1 The classical obstacle problem 1
1.1 The obstacle problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Existense and uniqueness of the solution of the obstacle problems . . . . . . . 4 1.3 W2 | - |
| dc.description.tableofcontents | p regularity of the solution of the classical obstacle problem . . . . . . . . . 6
1.4 C1 | - |
| dc.description.tableofcontents | 1 regularity of the solution of the classical obstacle problem . . . . . . . . . 8
2 Optimal regularity of solutions of obstacle problems 10 2.1 Model problems A | - |
| dc.description.tableofcontents | B | - |
| dc.description.tableofcontents | C and OT1 ?? OT2 . . . . . . . . . . . . . . . . . . . . . 10
2.2 ACF monotonicity formula and generalizations . . . . . . . . . . . . . . . . . 11 2.3 Optimal regularity in OT1 ?? OT2 . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Preliminary analysis of the free boundary 20 3.1 Nondegeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Lebesgue and Hausdo measures of the free boundary . . . . . . . . . . . . . 22 3.3 Classes of solutions, rescalings, and blowups . . . . . . . . . . . . . . . . . . 26 4 Obstacle problem for nonlinear second-order parabolic operator 29 4.1 Viscosity solution of parabolic equations . . . . . . . . . . . . . . . . . . . . . 29 4.2 The existence and the continuity theory . . . . . . . . . . . . . . . . . . . . . 30 | - |
| dc.format | application/pdf | - |
| dc.format.extent | 978851 bytes | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject | obstacle | - |
| dc.subject | obstacle problem | - |
| dc.subject | classical obstacle problem | - |
| dc.subject | Obstacle-type problem | - |
| dc.subject | free boundary | - |
| dc.subject | nonlinear second order parabolic operator | - |
| dc.subject.ddc | 510 | - |
| dc.title | Properties of obstacle problem and free boundary problem | - |
| dc.type | Thesis | - |
| dc.description.degree | Master | - |
| dc.citation.pages | ii, 34 | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2014-08 | - |
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