Change search
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • html
  • text
  • asciidoc
  • rtf
Positivity of Heat Kernels
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Partial di˙erential equations are a well-studied field of mathematics, and in this thesis we attempt to use some of the newer methods, including path integrals (also known as Feynman path integrals) and the so-called geometric approach, to find conditions for the heat kernel of a di˙erential operator on a certain form to be zero. We also derive a maximum principle, more general than the classical one, that allows for degenerate di˙erential operators, where the degeneracy is controlled by a Muckenhoupt weight. While we find the path integral method too deeply flawed to use, the geometric approach yields some results which show that the zeros of the coeÿcient of the second order term in the di˙erential operator control information transfer within the domain of the solution.

Abstract [sv]

Partiella di˙erentialekvationer utgör ett av de mest ingående studerade matematiska om-rådena. I denna uppsats försöker vi använda några nyare metoder, däribland vägintegraler (också kända som Feynmans vägintegraler) och den så kallade geometriska metoden, för att hitta villkor för värmekärnan för vissa di˙erentialoperatorer att vara lika med noll. Vi härle-der också en maximumprincip som är mer generell än den klassiska på så sätt att den tillåter degenererade di˙erentialoperatorer, där degenerationen kontrolleras av en Muckenhoupt-vikt. Medan vägintegralmetoden å ena sidan visar sig vara för behäftad med fel för att kunna använ-das, ger den geometriska metoden å andra sidan några resultat som visar att nollställena för koeÿcienten till andra ordningens term i di˙erentialoperatorn styr informationsöverföringen i lösningsområdet.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:059
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-251683OAI: oai:DiVA.org:kth-251683DiVA, id: diva2:1318063
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2019-05-25 Created: 2019-05-25 Last updated: 2019-05-25Bibliographically approved

Open Access in DiVA

fulltext(766 kB)23 downloads
File information
File name FULLTEXT01.pdfFile size 766 kBChecksum SHA-512
b3cd29a6b1bc8dc4b0ecb0cc4c1eb9894164bdd970b8d07827530dd4f18a09f719d16160b4a98c17a453c3f5ef40086100ed83af902799ef71f8f4e2d26aad5b
Type fulltextMimetype application/pdf

By organisation
Mathematics (Div.)
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 23 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 68 hits
CiteExportLink to record
Permanent link

Direct link
Cite
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
  • html
  • text
  • asciidoc
  • rtf