Abstract
For a second-order symmetric strongly elliptic operator A on a smooth bounded open set in Rn, the mixed problem is defined by a Neumann-type condition on a part σ+ of the boundary and a Dirichlet condition on the other part σ- We show a Kreǐn resolvent formula, where the difference between its resolvent and the Dirichlet resolvent is expressed in terms of operators acting on Sobolev spaces over σ+. This is used to obtain a new Weyl-type spectral asymptotics formula for the resolvent difference (where upper estimates were known before), namely sjj2/(n-1)→C0,+2/(n-1), where C0,+ is proportional to the area of σ+, in the case where A is principally equal to the Laplacian.
| Translated title of the contribution | Det blandede randværdiproblem, Krein resolvent-formler og spektralasymptotiske vurderinger |
|---|---|
| Original language | English |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 382 |
| Issue number | 1 |
| Pages (from-to) | 339–363 |
| Number of pages | 24 |
| ISSN | 0022-247X |
| Publication status | Published - 1 Oct 2011 |