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1	Eigenvalue Problem for the 1-Laplace Operator / Das Eigenwertproblem für den 1-Laplace-Operator Milbers, Zoja 27 March 2009 (has links) (PDF) We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations. / Wir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her. 1-Laplace nonsmooth critical point theory weak slope inner variations 1-Laplace nichtglatte Theorie kritischer Punkte weak slope innere Variationen ddc:510 rvk:SK 620
2	Eigenvalue Problem for the 1-Laplace Operator Milbers, Zoja 23 March 2009 (has links) We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variations. / Wir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her. info:eu-repo/classification/ddc/510 ddc:510
3	The Eigenvalue Problem of the 1-Laplace Operator Littig, Samuel 19 February 2015 (has links) (PDF) As a first aspect the thesis treats existence results of the perturbed eigenvalue problem of the 1-Laplace operator. This is done with the aid of a quite general critical point theory results with the genus as topological index. Moreover we show that the eigenvalues of the perturbed 1-Laplace operator converge to the eigenvalues of the unperturebed 1-Laplace operator when the perturbation goes to zero. As a second aspect we treat the eigenvalue problems of the vectorial 1-Laplace operator and the symmetrized 1-Laplace operator. And as a third aspect certain related parabolic problems are considered. 1-Laplace Operator Nichtglatte Theorie kritischer Punkte Geschlecht Störungsresultate Bifurkation Vektorwertiger Totalvariationsfluss Symmetrisierter 1-Laplace Operator BD 1-Laplace operator nonsmooth critical point theory genus perturbation bifurcation vectorial total variation flow symmetrized 1-Laplace operator BD ddc:510 rvk:SK 620
4	The Eigenvalue Problem of the 1-Laplace Operator: Local Perturbation Results and Investigation of Related Vectorial Questions Littig, Samuel 23 January 2015 (has links) As a first aspect the thesis treats existence results of the perturbed eigenvalue problem of the 1-Laplace operator. This is done with the aid of a quite general critical point theory results with the genus as topological index. Moreover we show that the eigenvalues of the perturbed 1-Laplace operator converge to the eigenvalues of the unperturebed 1-Laplace operator when the perturbation goes to zero. As a second aspect we treat the eigenvalue problems of the vectorial 1-Laplace operator and the symmetrized 1-Laplace operator. And as a third aspect certain related parabolic problems are considered. info:eu-repo/classification/ddc/510 ddc:510

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