Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/22128
Title: | Layer potential theory for the anisotropic Stokes system with variable $L_\infty$ symmetrically elliptic tensor coefficient |
Other Titles: | Layer potential theory for the anisotropic Stokes system with variable L∞ symmetrically elliptic tensor coefficient |
Authors: | Kohr, M Mikhailov, SE Wendland, WL |
Keywords: | potential theory;partial differential equations;anisotropic Stokes system;discontinuous coefficient;variational problem;Newtonian and layer potentials;weighted Sobolev spaces;transmission problems;exterior Dirichlet and Neumann problems;well-posedness |
Issue Date: | 7-May-2021 |
Publisher: | Wiley Periodicals LLC |
Citation: | Kohr, M., Mikhailov, S.E. and Wendland, W.L. (2021) 'Layer potential theory for the anisotropic Stokes system with variable L∞ symmetrically elliptic tensor coefficient', Mathematical Methods in the Applied Sciences, in press, pp. 1–34. doi: 10.1002/mma.7167. |
Abstract: | © 2021 The Authors. The aim of this paper is to develop a layer potential theory in L2-based weighted Sobolev spaces on Lipschitz bounded and exterior domains of Rn , n ≥ 3, for the anisotropic Stokes system with L∞ viscosity tensor coefficient satisfying an ellip- ticity condition for symmetric matrices with zero matrix trace. To do this, we explore equivalent mixed variational formulations and prove the well-posedness of some transmission problems for the anisotropic Stokes system in Lipschitz domains of Rn, with the given data in L2-based weighted Sobolev spaces. These results are used to define the volume (Newtonian) and layer potentials and to obtain their properties. Then, we analyze the well-posedness of the exterior Dirichlet and Neumann problems for the anisotropic Stokes system with L∞ symmetrically elliptic tensor coefficient by representing their solutions in terms of the obtained volume and layer potentials. |
URI: | https://bura.brunel.ac.uk/handle/2438/22128 |
DOI: | https://doi.org/10.1002/mma.7167 |
ISSN: | 0170-4214 |
Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
FullText.pdf | 745.72 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License