Flows and invariance for elliptic operators

2009/03/31 by A. F. M. ter Elst, Derek W. Robinson, ter Elst, A. F. M. +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP #msc:35J70

paper · pdf · doi:10.48550/arxiv.0903.5482

arxiv created 2009/03/31 · arxiv updated 2009/12/01

Abstract

Let S be the submarkovian semigroup on L₂(\bf R^d) generated by a self-adjoint, second-order, divergence-form, elliptic operator H with W^1,∞ coefficients c_kl. Further let Ω be an open subset of \bf R^d. Under mild conditions we prove that S leaves L₂(Ω) invariant if, and only if, it is invariant under the flows generated by the vector fields ∑_l=1^d c_kl ∂_l for all k.

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