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arXiv · 1202.0743

Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces

Michael Hinz·Michael Röckner·Alexander Teplyaev
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Abstract

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space $X$, our paper studies 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 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.

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Michael Hinz, Michael Röckner, Alexander Teplyaev. 2012-02-03. Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. https://arxiv.org/abs/1202.0743

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