Geodesic
Eigenvalue Estimate for a Weighted $\boldsymbol{p}$-Laplacian on Compact Manifolds with Boundary
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 70-75

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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, Neumann eigenvalue.
Mots-clés : gradient estimate 
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     author = {W. Lin-Feng and Zh. Yue-Ping},
     title = {Eigenvalue {Estimate} for a {Weighted} $\boldsymbol{p}${-Laplacian} on {Compact} {Manifolds} with {Boundary}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {70--75},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a6/}
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W. Lin-Feng; Zh. Yue-Ping. Eigenvalue Estimate for a Weighted $\boldsymbol{p}$-Laplacian on Compact Manifolds with Boundary. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 1, pp. 70-75. http://geodesic.mathdoc.fr/item/FAA_2012_46_1_a6/