3 papers
math.FA2020
Approximation of partial differential equations on compact resistance spaces
Michael Hinz, Melissa Meinert
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and d…
math.AP2018
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…
math.AP2017
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…