Collins M (2020)
Publication Language: English
Publication Type: Thesis
Publication year: 2020
This thesis is concerned with with questions of existence of variational solutions
and parabolic minimizers, respectively, to evolutionary parabolic variational problems
on metric measure spaces. First, we give
an overview on the properties of metric measure spaces and the calculus that we
make use of in the rest of the thesis.
Following the introduction of the metric setting, we obtain an existence result for parabolic
minimizers / variational solutions associated to integral functionals with a certain
growth behavior and boundary data with no dependence on the time variable.
The next part of the thesis is devoted to the existence of variational solutions for a similar setting but with data on the lateral boundary that depends on time.
Finally, we consider a Cauchy-Dirichlet problem for the total variation flow with time-independent boundary data.
APA:
Collins, M. (2020). Existence for Variational Solutions to Cauchy-Dirichlet Problems on Metric Measure Spaces (Dissertation).
MLA:
Collins, Michael. Existence for Variational Solutions to Cauchy-Dirichlet Problems on Metric Measure Spaces. Dissertation, 2020.
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