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 -