Flows and invariance for elliptic operators

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dc.creatorter Elst, A. F. M.
dc.creatorRobinson, Derek W.
dc.creatorSikora, Adam
dc.date2009-03-31
dc.date.accessioned2026-07-07T12:58:36Z
dc.date.available2026-07-07T12:58:36Z
dc.descriptionLet $S$ be the submarkovian semigroup on $L_2({\bf R}^d)$ generated by a self-adjoint, second-order, divergence-form, elliptic operator $H$ with $W^{1,\infty}$ coefficients $c_{kl}$. Further let $Ω$ be an open subset of ${\bf R}^d$. Under mild conditions we prove that $S$ leaves $L_2(Ω)$ invariant if, and only if, it is invariant under the flows generated by the vector fields $\sum_{l=1}^d c_{kl} \partial_l$ for all $k$.
dc.identifierhttps://arxiv.org/abs/0903.5482
dc.identifierhttp://arxiv.org/abs/0903.5482
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225298
dc.subjectAnalysis of PDEs
dc.subject35J70
dc.titleFlows and invariance for elliptic operators
dc.typetext

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