The Eigenvalue Problem of the 1-Laplace Operator
Institution: | Technische Universität Dresden |
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Department: | Fakultät Mathematik und Naturwissenschaften |
Degree: | PhD |
Year: | 2015 |
Record ID: | 1103821 |
Full text PDF: | http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-161044 |
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.