Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Details Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

2010-04-14

arxiv.org/abs/1004.2517v4

Mathematics

Analysis of PDEs

14 pages, Rewrite section 6 (the appendix) and correct a mistake in section 6

Scientific paper

In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters $u=\chi_{\lambda}^s f$ of Dirichlet Laplacian $\Delta_M$, $$c_s \lambda\|u\|_{L^2(M)} \leq \| \partial_{\nu}u \|_{L^2(\partial M)} \leq C_s \lambda \|u\|_{L^2(M)} $$ where the upper bound is true for any Riemannian manifold, and the lower bound is true for some small $0

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