Abstract
We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function. These estimates imply necessary and sufficient conditions for the validity of the classical one-term Weyl formula for the counting function and, under certain restrictions, give an order sharp remainder estimate in this formula.
| Translated title of the contribution | Sharp remainder estimates in the Weyl formula for the Neumann Laplacian on a class of planar regions |
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| Original language | English |
| Pages (from-to) | 21 - 41 |
| Number of pages | 21 |
| Journal | Journal of Functional analysis |
| Volume | 250 (1) |
| DOIs | |
| Publication status | Published - Sept 2007 |