$L^p$ Spectral Radius Estimates for the Lamé System on an Infinite Sector
Johnson, Tomas
Experiment. Math., Tome 17 (2008) no. 1, p. 333-339 / Harvested from Project Euclid
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We prove, using interval analysis methods, that the $L^2$, $L^4$, and $L^8$ spectral radii of the traction double layer potential operator associated with the Lam\'e system on an infinite sector in $\mathbb R}^2$ are within $2.5 x 10^-3$, $10^-2$, and $10^-2$, respectively, from a certain conjectured value that depends explicitly on the aperture of the sector and the Lamé moduli of the system. We also indicate how to extend these results to $L^p$ for entire intervals of $p$, $p\geq2$.
Publié le : 2008-05-15
Classification:  Lamé system,  traction conormal derivative,  spectral radius,  interval analysis,  computer-aided proof,  35J25,  47-04,  45E05,  65G20 
@article{1227121386,
     author = {Johnson, Tomas},
     title = {$L^p$ Spectral Radius Estimates for the Lam\'e System on an Infinite Sector},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 333-339},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227121386}
}

Johnson, Tomas. $L^p$ Spectral Radius Estimates for the Lamé System on an Infinite Sector. Experiment. Math., Tome 17 (2008) no. 1, pp.  333-339. http://gdmltest.u-ga.fr/item/1227121386/