H-compactness of elliptic operators on weighted Riemannian Manifolds
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds with rapidly oscillating metrics. We appeal to the notion of H-convergence introduced by Murat and Tartar. In our main result we establish an H-compactness result that applies to elliptic operators with measurable, uniformly elliptic coefficients on weighted Riemannian manifolds. We further discuss the special case of ``locally periodic'' coefficients and study the asymptotic spectral behavior of compact submanifolds of $\mathbb R^n$ with rapidly oscillating geometry.
Details
Original language | English |
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Pages (from-to) | 161-191 |
Journal | Interdisciplinary Information Sciences |
Volume | 25 |
Issue number | 2 |
Publication status | Published - 2 Dec 2019 |
Peer-reviewed | Yes |
Keywords
Keywords
- math.AP, math.DG, 35B27, 58J05, 58J65