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dc.contributor.advisorBartsch, Thomas
dc.contributor.advisorAhmedou, Mohameden
dc.contributor.authorFiernkranz, Tim
dc.date.accessioned2021-12-08T14:31:17Z
dc.date.available2021-12-08T14:31:17Z
dc.date.issued2021
dc.identifier.urihttps://jlupub.ub.uni-giessen.de//handle/jlupub/371
dc.identifier.urihttp://dx.doi.org/10.22029/jlupub-307
dc.description.abstractFor $2\le N\in \N$ and $\G_i\in \R\setminus\{0\}$ we proof that functions of the form $$ H_\G (p_1,\dots, p_N) = \sum_{i\ne j} \G_i\G_j G(p_i,p_j) + \sum_{i=1}^N \G_i^2 R(p_i) , $$ admit critical points under various circumstances. The $p_i$ will either belong to an open, bounded subset $\gO\subset \R^d$ with smooth boundary for $d \ge 3$ or to a compact, two dimensional, riemanian manifold $(\gS ,g )$. Furthermore, $G$ is a (Dirichlet) Green's function of the negative Laplacian $-\gD$ associated to $\gO$ or $(\gS, g)$ and $R$ is its Robin's function.\\ For the case of an open set, we also consider the function $\gr$ that is the least eigenvalue of the matrix $$ (M(x_1,\dots,x_N))_{i,j=1}^N := \begin{cases} -G(x_i , x_j),& i\ne j\\ R(x_i),& i=j . \end{cases} $$ To achieve the critical points, we also calculate appropriate approximations of the Green's function and Robin's function when close to their singularities.de_DE
dc.language.isoende_DE
dc.subjectCritical Pointsde_DE
dc.subjectVortex Dynamicsde_DE
dc.subjectGreens Functionde_DE
dc.subject.ddcddc:510de_DE
dc.titleCritical Points of Kirchhoff-Routh-Type Functionsde_DE
dc.typedoctoralThesisde_DE
dcterms.dateAccepted2021-11-02
local.affiliationFB 07 - Mathematik und Informatik, Physik, Geographiede_DE
thesis.levelthesis.doctoralde_DE


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