Continuity in weak topology and extremal problems of eigenvalues of the $p$-Laplacian
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- by Ping Yan and Meirong Zhang PDF
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Abstract:
We will study the dependence of eigenvalues of the one-dimensional $p$-Laplacian on potentials or weights. Two results are obtained. One is the continuity of eigenvalues in potentials with respect to the weak topologies of $L^\gamma$ spaces, $1\le \gamma \le \infty$, and the other is the continuous differentiability of eigenvalues in potentials with respect to $L^\gamma$ norms. As applications, we will study some extremal problems of eigenvalues by developing some analytical methods.References
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Additional Information
- Ping Yan
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: pyan@math.tsinghua.edu.cn
- Meirong Zhang
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China – and – Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, People’s Republic of China
- Email: mzhang@math.tsinghua.edu.cn
- Received by editor(s): September 12, 2008
- Received by editor(s) in revised form: March 17, 2009
- Published electronically: November 5, 2010
- Additional Notes: This research was supported by the National Basic Research Program of China (Grant no. 2006CB805903), the National Natural Science Foundation of China (Grant no. 10531010) and the 111 Project of China (2007).
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 2003-2028
- MSC (2010): Primary 47J10, 34L15; Secondary 58C07, 58C40
- DOI: https://doi.org/10.1090/S0002-9947-2010-05051-2
- MathSciNet review: 2746673