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dc.contributorMas Blesa, Albert
dc.contributor.authorRodés Bachs, Clàudia
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractThis work aims to go in-depth in the study of Rayleigh-Faber-Krahn inequality and its proof. This inequality solves the shape optimization problem for the first Dirichlet eigenvalue under a volume constraint. Its proof will be addressed using Rayleigh quotient and Pólya-Szegö inequality, that need from Sobolev spaces to be rigorously understood. Besides, there is an enormous attention to applications of Rayleigh-Faber-Krahn inequality. Specifically, branches such as music, finance, fluids' transport, and quantum mechanics will be studied. Finally, some concrete calculus will be seen: the wave equation will be compared in 2 dimensions and in n dimensions over a generic parallelepiped and a ball through MATLAB. With the several examples and the concrete calculus, we aim to determine which domain has the smallest first Dirichlet eigenvalue among various of the same volume, and hence, motivate the Rayleigh-Faber-Krahn inequality.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
dc.subject.lcshDifferential equations, Partial
dc.subject.otherRayleigh-Faber-Krahn inequality
dc.subject.otherEigenvalue problem
dc.subject.otherDirichlet homogeneous eigenvalue problem
dc.subject.otherSobolev spaces
dc.subject.otherPólya-Szegö inequality
dc.subject.otherRayleigh quotient
dc.subject.otherReactive substance
dc.subject.otherQuantum mechanics
dc.subject.otherN-dimensional calculus
dc.titleThe Rayleigh-Faber-Krahn inequality and applications
dc.typeBachelor thesis
dc.subject.lemacEquacions en derivades parcials
dc.subject.amsClassificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeGRAU EN MATEMÀTIQUES (Pla 2009)

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