Inverse iteration for $p$-ground states
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- by Ryan Hynd and Erik Lindgren PDF
- Proc. Amer. Math. Soc. 144 (2016), 2121-2131 Request permission
Abstract:
We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for $p\in (1,\infty )$ and a given domain $\Omega \subset \mathbb {R}^n$, we analyze a scheme that allows us to approximate the smallest value the ratio $\int _\Omega |D\psi |^pdx/\int _\Omega |\psi |^pdx$ can assume for functions $\psi$ that vanish on $\partial \Omega$. The scheme in question also provides a natural way to approximate minimizing $\psi$. Our analysis also extends in the limit as $p\rightarrow \infty$ and thereby fashions a new approximation method for ground states of the infinity Laplacian.References
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Additional Information
- Ryan Hynd
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- MR Author ID: 789875
- Email: rhynd@math.upenn.edu
- Erik Lindgren
- Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
- Email: eriklin@kth.se
- Received by editor(s): March 5, 2015
- Received by editor(s) in revised form: May 30, 2015, and June 9, 2015
- Published electronically: September 11, 2015
- Additional Notes: The first author was partially supported by NSF grant DMS-1301628. The second author was supported by the Swedish Research Council, grant no. 2012-3124, and partially supported by the Royal Swedish Academy of Sciences.
- Communicated by: Jeremy Tyson
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2121-2131
- MSC (2010): Primary 35J70, 35J60, 35P30
- DOI: https://doi.org/10.1090/proc/12860
- MathSciNet review: 3460172