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Degenerate elliptic operators: capacity, flux and separation | Derek W. Robinson
; Adam Sikora
; | Date: |
14 Jan 2006 | Subject: | Analysis of PDEs | Abstract: | Let $S={S_t}_{tgeq0}$ be the semigroup generated on $L_2(Ri^d)$ by a self-adjoint, second-order, divergence-form, elliptic operator $H$ with Lipschitz continuous coefficients. Further let $Omega$ be an open subset of $Ri^d$ with Lipschitz continuous boundary $partialOmega$. We prove that $S$ leaves $L_2(Omega)$ invariant if, and only if, the capacity of the boundary with respect to $H$ is zero or if, and only if, the energy flux across the boundary is zero. The global result is based on an analogous local result. | Source: | arXiv, math/0601351 | Services: | Forum | Review | PDF | Favorites |
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