Newtonian and single layer potentials for the Stokes system with $L^{\infty}$ coefficients and the exterior Dirichlet problem

Mirela Kohr; Sergey E. Mikhailov; Wolfgang L. Wendland

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arXiv · 1807.10222

Newtonian and single layer potentials for the Stokes system with $L^{\infty}$ coefficients and the exterior Dirichlet problem

Mirela Kohr·Sergey E. Mikhailov·Wolfgang L. Wendland

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Abstract

A mixed variational formulation of some problems in $L^2$-based Sobolev spaces is used to define the Newtonian and layer potentials for the Stokes system with $L^{\infty}$ coefficients on Lipschitz domains in ${\mathbb R}^3$. Then the solution of the exterior Dirichlet problem for the Stokes system with $L^{\infty}$ coefficients is presented in terms of these potentials and the inverse of the corresponding single layer operator.

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Mirela Kohr, Sergey E. Mikhailov, Wolfgang L. Wendland. 2018-07-26. Newtonian and single layer potentials for the Stokes system with $L^{\infty}$ coefficients and the exterior Dirichlet problem. https://arxiv.org/abs/1807.10222

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