Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces
By Michael Hinz, Michael Röckner, Alexander Teplyaev. 2012
55 citations recorded by the source corpus.
Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X, our paper studies elements of vector analysis, Lp-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3461fd6fc6aafad198cfc091cee17798cb8a72a5
How researchers see this paper
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In Applied Mathematics
- Patricia Alonso-Ruiz
- Luke G. Rogers
- Fabrice Baudoin
- Li Chen
- Alexander Teplyaev
- Nageswari Shanmugalingam
- Anders Bjorn
- Luigi Ambrosio
In Computational Theory and Mathematics
In Mathematical Physics
- Patricia Alonso-Ruiz
- Luke G. Rogers
- Fabrice Baudoin
- Li Chen
- Alexander Teplyaev
- Nageswari Shanmugalingam
- Alexander Schied
- Anders Bjorn
Citations in the corpus
- Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “One might expect that if u ∈ BV (X) then, following [46, 47], Du could be defined as a vector valued Borel measure, however the details of this construction are outside of the scope of this article.”