Semiclassical asymptotics for a class of singular Schrödinger operators
Let Ω ⊂ â„^d be bounded with C¹ boundary. In this paper we consider Schrödinger operators −Δ + W on Ω with W(x) ≈ dist(x,∂Ω)â»Â² as dist(x,∂Ω) → 0. Under weak assumptions on W we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators. We are deeply g...
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| Format: | Report |
| Language: | unknown |
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arXiv
2021
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| Online Access: | https://doi.org/10.48550/arXiv.2010.05417 |
| Summary: | Let Ω ⊂ â„^d be bounded with C¹ boundary. In this paper we consider Schrödinger operators −Δ + W on Ω with W(x) ≈ dist(x,∂Ω)â»Â² as dist(x,∂Ω) → 0. Under weak assumptions on W we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators. We are deeply grateful to Ari Laptev for sharing his fascination for spectral estimates and Hardy's inequality with us and we would like to dedicate this paper to him on the occasion of his 70th birthday. U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and Knut and Alice Wallenberg Foundation grant KAW 2018.0281 (S.L.) are acknowledged. Submitted - 2010.05417.pdf |
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