The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt



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 titelDet blandede randværdiproblem, Krein resolvent-formler og spektralasymptotiske vurderinger
OriginalsprogEngelsk
TidsskriftJournal of Mathematical Analysis and Applications
Vol/bind382
Udgave nummer1
Sider (fra-til)339–363
Antal sider24
ISSN0022-247X
StatusUdgivet - 2011

ID: 33793950