Layer potential theory for the anisotropic Stokes system with variable $L_\infty$ symmetrically elliptic tensor coefficient
| Autor: | Sergey E. Mikhailov, Wolfgang L. Wendland, Mirela Kohr |
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| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
Mathematics::Analysis of PDEs anisotropic Stokes system weighted Sobolev spaces 01 natural sciences Potential theory potential theory Newtonian and layer potentials well-posedness partial differential equations exterior Dirichlet and Neumann problems Tensor 0101 mathematics Layer (object-oriented design) Anisotropy transmission problems Variable (mathematics) Mathematics Mathematical physics Partial differential equation discontinuous coefficient 010102 general mathematics General Engineering variational problem Integral equation 010101 applied mathematics Nonlinear system |
| Zdroj: | Mathematical Methods in the Applied Sciences. |
| ISSN: | 1099-1476 0170-4214 |
| DOI: | 10.1002/mma.7167 |
| Popis: | © 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. EPSRC grant EP/M013545/1: "Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs"; Babeş-Bolyai University research grant AGC35124/31.10.2018; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy-EXC 2075-390740016. |
| Databáze: | OpenAIRE |
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