The spectral behavior of the difference between the resolvents of two realizations of a second-order strongly elliptic symmetric differential operator defined by different Robin conditions and , can in the case where all coefficients are be determined by use of a general result by the author in 1984 on singular Green operators. We here treat the problem for nonsmooth , showing that if and are in , the s-numbers satisfy for all . This improves a recent result for by Behrndt et al., that for , under a hypothesis of boundedness of . Moreover, we show that if and are in for some , with jumps at a smooth hypersurface, then for , with a constant defined from the principal symbol of and . We also show that the usual principal spectral asymptotic estimate for pseudodifferential operators of negative order on a closed manifold extends to products of pseudodifferential operators of negative order interspersed with piecewise continuous functions.
Cite this article
Gerd Grubb, Spectral asymptotics for Robin problems with a discontinuous coefficient. J. Spectr. Theory 1 (2011), no. 2, pp. 155–177DOI 10.4171/JST/7