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タイトル: | Estimates of Dirichlet Eigenvalues for Degenerate Elliptic Operators (Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics) |
著者: | Chen, Hua Luo, Peng |
キーワード: | 35J70 35P15 Dirichlet eigenvalues finitely degenerate elliptic operators infinitely degenerate elliptic operators Hörmander's condition sub-elliptic estimate logarithmic regularity estimate |
発行日: | Oct-2017 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
誌名: | 数理解析研究所講究録別冊 |
巻: | B67 |
開始ページ: | 1 |
終了ページ: | 24 |
抄録: | Let Ω be a bounded open domain in Rn with smooth boundary and X = (X1, X2, …, Xm) be a system of real smooth vector fields defined on Ω with the boundary ∂Ω which is non-characteristic for X. If X satisfies the H ormander's condition, then the vector fields is finite degenerate and the sum of square operator △X = Σm j=1 X2 j is a finitely degenerate elliptic operator, otherwise the operator -△X is called infinitely degenerate. If λj is the jth Dirichlet eigenvalue for -△X on Ω, then this paper shall study the lower bound estimates for λj. Firstly, by using the sub-elliptic estimate directly, we shall give a simple lower bound estimates of λj for general finitely degenerate △X which is polynomial increasing in j. Secondly, if △X is so-called Grushin type degenerate elliptic operator, then we can give a precise lower bound estimates for λj. Finally, by using logarithmic regularity estimate, for infinitely degenerate elliptic operator △X we prove that the lower bound estimates of λj will be logarithmic increasing in j. |
記述: | "Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics". May 27~29, 2016. edited by Hisashi Okamoto, Yoshio Tsutsumi, Naomasa Ueki, Tadayoshi Adachi and Senjo Shimizu. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. |
著作権等: | © 2017 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved. |
URI: | http://hdl.handle.net/2433/243702 |
出現コレクション: | B67 Workshop on the Boltzmann Equation, Microlocal Analysis and Related Topics |
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