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Symmetry in a free boundary problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2023 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Symmetri i ett frirandsproblem (Swedish)
Abstract [en]

We consider a variational formulation of a Bernoulli-type free boundary problem for the Laplacian operator with discontinuous boundary data. We show the existence of a weak solution to the problem. Moreover, we show that the solution has symmetry properties inherited by symmetric data. These results are achieved through the use of comparison arguments, the celebrated method of moving planes, and several elaborated techniques from existing literature.

Abstract [sv]

Vi studerar ett Bernoulli frirandsproblem för Laplaceoperatorn med diskontinuerliga randdata. Detta görs via en variationsformulering av problemet. Vi visar att en svag lösning existerar för problemet. Utöver det visar vi bland annat att den svaga lösningen har symmetriegenskaper. Dessa resultat uppnås genom jämförelseargument, den välkända "moving-plane” metoden, samt flera utarbetade tekniker från befintlig litteratur.

Place, publisher, year, edition, pages
2023. , p. 41
Series
TRITA-SCI-GRU ; 2023:452
Keywords [en]
Analysis of PDEs, Bernoulli-type boundary condition, free boundary problem, Laplacian operator, method of moving planes, symmetry
Keywords [sv]
Analys av PDEs, Bernoulli-typ randvärde, frirandsproblem, Laplaceoperatorn, moving-plane metoden, symmetri
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-344220OAI: oai:DiVA.org:kth-344220DiVA, id: diva2:1843169
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2024-03-22 Created: 2024-03-08 Last updated: 2024-03-22Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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