Degenerate elliptic operators

capacity, flux and separation

Derek W. Robinson, Adam Sikora

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)385-408
Number of pages24
JournalJournal of the Ramanujan Mathematical Society
Issue number4
Publication statusPublished - 2007
Externally publishedYes

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