Vector analysis for local Dirichlet forms and quasilinear PDE and SPDE on fractals

Details Vector analysis for local Dirichlet forms and quasilinear PDE and SPDE on fractals Vector analysis for local Dirichlet forms and quasilinear PDE and SPDE on fractals

2012-02-03

arxiv.org/abs/1202.0743v2

Mathematics

Functional Analysis

Scientific paper

Starting with local regular symmetric Dirichlet forms, our paper studies some elements of vector analysis, $L_p$-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 some SPDE in variational form by classical methods. The setup is sufficiently general to be applied to Dirichlet forms on fractal spaces such as finitely ramified fractals and Sierpinski carpets.

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