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Authors
Affiliations
1 Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, AU
2 Department of Mathematical Sciences, New Mexico State University, P.O. Box 30001, Las Cruces, NM 88003-8001, US
Source
Journal of the Ramanujan Mathematical Society, Vol 22, No 4 (2007), Pagination: 385–408
Abstract
Let S = {St}t≥0 be the semigroup generated on L2(Rd) by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients. Further let Ω be an open subset of Rd with Lipschitz continuous boundary ∂Ω. We prove that S leaves L2(Ω) 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.