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Potential theoretic skeletons for two-dimensional heavy bodies
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Potential theoretic skeletons (also called mother bodies) are minimal

bodies that generate the same gravitational potential as some given heavy

body. They are minimal in the sense that their support have Lebesgue

measure zero, and must satisfy some additional requirements. A mother

body does not necessarily exist for a body, and if it does, it is not necessarily

unique. Despite these issues, the study of these objects is motivated by

inverse problems of geophysics and Hele-Shaw flows. In this text mother

bodies are studied from a potential theoretic point of view, as well as with

PDE methods.

Abstract [sv]

Potentialteoretiska skelett (som även kallas moderkroppar) är minimala

kroppar som ger upphov till samma gravitationspotential som en

given massiv kropp. Moderkroppar är minimala i det avseendet att deras

stöd har Lebesguemått noll, och att de uppfyller några ytterligare krav.

Vissa kroppar har flera moderkroppar medan andra saknar någon helt.

Trots detta studeras dessa föremål med anledning från inversa problem i

geofysik samt Hele-Shaw-flöden. I den här texten angrips problemet att

hitta moderkroppar från både ett potentialteoretiskt perspektiv och med

hjälp av PDE-metoder.

Place, publisher, year, edition, pages
2012. , 17 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-103603OAI: diva2:560857
Available from: 2012-11-12 Created: 2012-10-16 Last updated: 2014-10-16Bibliographically approved

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