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

Hinz M, Röckner M, Teplyaev A (2013)
Stochastic Processes And Their Applications 123(12): 4373-4406.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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. (C) 2013 Elsevier B.V. All rights reserved.
Stichworte
p-Laplacian; p-energy; Fractals; measure spaces; Metric; Quasilinear PDE and SPDE; Dirichlet forms; Vector analysis
Erscheinungsjahr
2013
Zeitschriftentitel
Stochastic Processes And Their Applications
Band
123
Ausgabe
12
Seite(n)
4373-4406
ISSN
0304-4149
Page URI
https://pub.uni-bielefeld.de/record/2635459

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Hinz M, Röckner M, Teplyaev A. Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. Stochastic Processes And Their Applications. 2013;123(12):4373-4406.
Hinz, M., Röckner, M., & Teplyaev, A. (2013). Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. Stochastic Processes And Their Applications, 123(12), 4373-4406. doi:10.1016/j.spa.2013.06.009
Hinz, M., Röckner, M., and Teplyaev, A. (2013). Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. Stochastic Processes And Their Applications 123, 4373-4406.
Hinz, M., Röckner, M., & Teplyaev, A., 2013. Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. Stochastic Processes And Their Applications, 123(12), p 4373-4406.
M. Hinz, M. Röckner, and A. Teplyaev, “Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces”, Stochastic Processes And Their Applications, vol. 123, 2013, pp. 4373-4406.
Hinz, M., Röckner, M., Teplyaev, A.: Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces. Stochastic Processes And Their Applications. 123, 4373-4406 (2013).
Hinz, Michael, Röckner, Michael, and Teplyaev, Alexander. “Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces”. Stochastic Processes And Their Applications 123.12 (2013): 4373-4406.

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