6 research outputs found
Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions
We introduce an iterative method for computing the first eigenpair
for the -Laplacian operator with homogeneous Dirichlet
data as the limit of as , where
is the positive solution of the sublinear Lane-Emden equation
with same boundary data. The method is
shown to work for any smooth, bounded domain. Solutions to the Lane-Emden
problem are obtained through inverse iteration of a super-solution which is
derived from the solution to the torsional creep problem. Convergence of
to is in the -norm and the rate of convergence of
to is at least . Numerical evidence is
presented.Comment: Section 5 was rewritten. Jed Brown was added as autho
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow
\|u\|^p_{W^{1,p}(\Omega)} that are independent of . This estimates
generalized those of [3] for general . Here is the
critical exponent for the immersion and is the space dimension. Then we
apply our results first to prove existence of positive solutions to a nonlinear
elliptic problem with a nonlinear boundary condition with critical growth on
the boundary, generalizing the results of [16]. Finally, we study an optimal
design problem with critical exponent.Comment: 22 pages, submitte