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Regularitet för semilinjära elliptiska partiella differentialekvationer med kritiska Sobolevexponenter
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Regularity of semilinear elliptic partial differential equations with critical Sobolev exponents (English)
Abstract [sv]

Vi studerar regularitet och existens av lösningar i Sobolevrum till semilinjära elliptiska partiella differentialekvationer i begränsade öppna områden. Vi identifierar ett tillväxtvillkor på den ickelinjära termen som är tillräckligt för att påvisa existens av lösningar givet att området och randvillkoren är regulära. Det är två huvudsakliga steg i metoden. Först reducerar vi den semilinjära ekvationen till en linjär ekvation som vi löser. Sedan använder vi en topologisk fixpunktsats för att bevisa att det existerar en lösning till den semilinjära ekvationen.

Abstract [en]

We study the regularity and existence of solutions in Sobolev spaces to semilinear elliptic partial differential equations in bounded domains. We identify a growth condition on the nonlinear term that suffices to prove existence and uniqueness of solutions provided the domain and boundary conditions are adequately regular. There are two major steps. First we reduce the semilinear equation to a linear equation that we solve. Secondly we apply a topological fixed point theorem to prove the existence of a solution to the semilinear equation.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:111
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254695OAI: oai:DiVA.org:kth-254695DiVA, id: diva2:1334760
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Examiners
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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