Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON STABILITY OF A TRANSFMISSION PROBLEM

  • Published : 1997.08.01
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Abstract

We investigate the bahivor of the gradient of solutions to the refraction equation $div(( 1+ (k - 1)_\chi D)\nabla u) = 0$ under perturbation of domain D. If $u_h$ are solutions to the refraction equation corresponding to subdomains D and $D_h$ of a domain $\Omega$ in 2 dimensional plane with the same Neumann data on $\partial\Omega$, respectively, we prove that $\left\$\mid$ \nabla(u - u_h) \right\$\mid$_{L^2(\Omega)} \leq C\sqrt{dist(D, D_h)}$ where $dist(D, D_h)$ is the Hausdorff distance between D and $D_h$. We also show that this is the best possible result.

Keywords

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