Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces |
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Authors: | Michael Hinz Michael Röckner Alexander Teplyaev |
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Institution: | 1. Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009, USA;2. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany |
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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, 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. |
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Keywords: | Dirichlet forms Vector analysis Quasilinear PDE and SPDE Metric measure spaces Fractals p-energy" target="_blank">gif" overflow="scroll">p-energy p-Laplacian" target="_blank">gif" overflow="scroll">p-Laplacian |
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