Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vector analysis on fractals and applications   The paper surveys some recent results concerning vector analysis on fractals.
We start with a local regular Dirichlet form and use the framework of 1-forms
and derivations introduced by Cipriani and Sauvageot to set up some elements of
a related vector analysis in weak and non-local formulation. This allows to
study various scalar and vector valued linear and non-linear partial
differential equations on fractals that had not been accessible before.
Subsequently a stronger (localized, pointwise or fiberwise) version of this
vector analysis can be developed, which is related to previous work of Kusuoka,
Kigami, Eberle, Strichartz, Hino, Ionescu, Rogers, R\"ockner, and the authors.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ