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INVERSE ITERATION FOR p-GROUND STATES.
- Source :
- Proceedings of the American Mathematical Society; May2016, Vol. 144 Issue 5, p2121-2131, 11p
- Publication Year :
- 2016
-
Abstract
- We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p ∈ (1, ∞) and a given domain Ω ⊂ ℝ<superscript>n</superscript>, we analyze a scheme that allows us to approximate the smallest value the ratio ∫<subscript>Ω</subscript> |Dψ|<superscript>p</superscript>dx/ ∫<subscript> Ω</subscript>|ψ|<superscript>p</superscript>dx can assume for functions ψ that vanish on ∂Ω. The scheme in question also provides a natural way to approximate minimizing ψ. Our analysis also extends in the limit as p → ∞ and thereby fashions a new approximation method for ground states of the infinity Laplacian. [ABSTRACT FROM AUTHOR]
- Subjects :
- SYMMETRIC matrices
MATRICES (Mathematics)
MATHEMATICS
EIGENVALUES
EIGENANALYSIS
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 144
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 113145131
- Full Text :
- https://doi.org/10.1090/proc/12860