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On the existence of optimal shapes in architecture
Michael Hinz, Frédéric Magoulès, Rozanova-Pierrat Anna +2
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initi…
Non-Lipschitz uniform domain shape optimization in linear acoustics
Michael Hinz, Anna Rozanova-Pierrat, Alexander Teplyaev
We introduce new parametrized classes of shape admissible domains in R^n , n 2, and prove that they are compact with respect to the convergence in the sense of characteristic…
Sobolev spaces and calculus of variations on fractals
Michael Hinz, Dorina Koch, Melissa Meinert
The present note contains a review of -energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then use…
A note on Neumann problems on graphs
Michael Hinz, Michael Schwarz
We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvab…
On the viscous Burgers equation on metric graphs and fractals
Michael Hinz, Melissa Meinert
We study a formulation of Burgers equation on the Sierpinski gasket, which is the prototype of a p.c.f. self-similar fractal. One possibility is to implement Burgers equation as a…