TY - JOUR

T1 - Degenerate elliptic operators

T2 - capacity, flux and separation

AU - Robinson, Derek W.

AU - Sikora, Adam

PY - 2007

Y1 - 2007

N2 - Let S = {S}t≥o 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 dΩ. 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.

AB - Let S = {S}t≥o 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 dΩ. 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.

UR - http://www.scopus.com/inward/record.url?scp=84930683729&partnerID=8YFLogxK

UR - https://www.researchonline.mq.edu.au/vital/access/manager/Repository/mq:16824

M3 - Article

AN - SCOPUS:84930683729

SN - 0970-1249

VL - 22

SP - 385

EP - 408

JO - Journal of the Ramanujan Mathematical Society

JF - Journal of the Ramanujan Mathematical Society

IS - 4

ER -