Ellipticity and Ergodicity
نویسندگان
چکیده
Let S = {St}t≥0 be the submarkovian semigroup on L2(R ) generated by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients cij . Further let Ω be an open subset of R . We prove that S leaves L2(Ω) invariant if, and only if, it is invariant under the flows generated by the vector fields Yi = ∑d j=1 cij∂j .
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