Affiliation:
1. Department of Mathematics and Maxwell Institute for Mathematical Sciences Heriot-Watt University, Edinburgh EH14 4AS, UK
Abstract
For
, the eigenfunctions of the nonlinear eigenvalue problem associated with the one-dimensional
q
-Laplacian are known to form a Riesz basis of
L
2
(0,1). We examine in this paper the approximation properties of this family of functions and its dual, and establish a non-orthogonal spectral method for the
p
-poisson boundary value problem and its corresponding parabolic time-evolution initial value problem with stochastic forcing. The principal objective of our analysis is the determination of optimal values of
q
for which the best approximation is achieved for a given
p
problem.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
10 articles.
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