Brief communications

Eigenvalue Estimate for a Weighted $p$-Laplacian on Compact Manifolds with Boundary

W. Lin-Feng, Zh. Yue-Ping

Nantong University, School of Science

Abstract: Let $(M^n,g)$ be a compact Riemannian manifold with convex boundary, let $d\mu=e^{h(x)}\,dV(x)$ be a weighted measure on $M$, and let $\Delta_{\mu,p}$ be the corresponding weighted $p$-Laplacian on $M$. We obtain a lower bound for the first nonzero Neumann eigenvalue of $\Delta_{\mu,p}$.

Keywords: weighted $p$-Laplacian, Bakry–Émery curvature, gradient estimate, Neumann eigenvalue.

UDC: 517.9

Received: 19.03.2010

DOI: 10.4213/faa3060

 English version: Functional Analysis and Its Applications, 2012, 46:1, 58–61

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