ArticleApproximation of the least Rayleigh quotient for degree p homogeneous functionals
The third result is Erik C Lindgren age 30s in Pismo Beach, CA. They have also lived in San Luis Obispo, CA and Makawao, HI. Erik is related to Dane Andrew Lindgren and Mark E Lindgren as well as 2 additional people. Select this result to view Erik C Lindgren's phone number, address, and more. Product Design- Portland, OR. Erik lindgren design. Erik LINDGREN Cited by 446 of Uppsala University Hospital, Uppsala Read 11 publications Contact Erik LINDGREN.
Journal of Functional Analysis 272 (12), 2017
Posted by:
Erik Lindgren Google
We present two novel methods for approximating minimizers of the abstract Rayleigh quotient $Phi(u)/ u ^p$. Here $Phi$ is a strictly convex functional on a Banach space with norm $ cdot $, and $Phi$ is assumed to be positively homogeneous of degree $pin (1,infty)$. Minimizers are shown to satisfy $partial Phi(u)- lambdamathcal{J}_p(u)ni 0$ for a certain $lambdain mathbb{R}$, where $mathcal{J}_p$ is the subdifferential of $frac{1}{p} cdot ^p$. The first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy $$ partial Phi(u_k)- mathcal{J}_p(u_{k-1})ni 0 quad (kin mathbb{N}). $$ The second method is based on the large time behavior of solutions of the doubly nonlinear evolution $$ mathcal{J}_p(dot v(t))+partialPhi(v(t))ni 0 quad(a.e.;t>0) $$ and more generally $p$-curves of maximal slope for $Phi$. We show that both schemes have the remarkable property that the Rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of $Phi(u)/ u ^p$. These results are new even for Hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in Sobolev spaces.
Erik Lindgren
Lindgren is an Iowa born artist and illustrator specializing in transportation art, models and photography. His passion for both automobiles and railroad history has driven his creative side and resulted in numerous commissions from clients around the country. Erik now resides in Arvada, Colorado with his wife and children. View the profiles of professionals named 'Erik Lindgren' on LinkedIn. There are 100+ professionals named 'Erik Lindgren', who use LinkedIn to exchange information, ideas, and opportunities.