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 Kreĭn 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
| Bidragets oversatte titel | Det blandede randværdiproblem, Krein resolvent-formler og spektralasymptotiske vurderinger |
|---|---|
| Originalsprog | Engelsk |
| Tidsskrift | Journal of Mathematical Analysis and Applications |
| Vol/bind | 382 |
| Udgave nummer | 1 |
| Sider (fra-til) | 339–363 |
| Antal sider | 24 |
| ISSN | 0022-247X |
| Status | Udgivet - 1 okt. 2011 |