<p>Using the finite element software FEMLAB® solutions are computed to Dirichlet problems for the Infinity-Laplace equation ∆∞(<i>u</i>) ≡ <i>u</i>²_x<i>u</i>_xx+ 2<i>u</i>_x<i>u</i>_y<i>u</i>_xy+<i>u</i>²_y<i>u</i>_yy= 0. For numerical reasons ∆<i>q</i>(<i>u</i>) = div (|▼<i>u</i>|<i>q</i>▼<i>u</i>)<i> = </i>0, which (formally) approaches as ∆∞(<i>u</i>) = 0 as <i>q</i> → ∞, is used in computation. A parametric nonlinear solver is used, which employs a variant of the damped Newton-Gauss method. The analysis of the experiments is done using the known theory of solutions to Dirichlet problems for ∆∞(<i>u</i>) = 0, which includes AMLEs (Absolutely Minimizing Lipschitz Extensions), sets of uniqueness, critical segments and lines of singularity. From the experiments one main conjecture is formulated: For Dirichlet problems, which have a non-constant boundary function, it is possible to predict the structure of the lines of singularity in solutions in the Infinity-Laplace case by examining the corresponding Laplace case.</p>

Using the finite element software FEMLAB® solutions are computed to Dirichlet problems for the Infinity-Laplace equation ∆∞(u) ≡ u2xuxx + 2uxuyuxy + u2yuyy = 0. For numerical reasons ∆q(u) = div (|▼u|q▼u) = 0, which (formally) approaches as ∆∞(u) = 0 as q → ∞, is used in computation. A parametric nonlinear solver is used, which employs a variant of the damped Newton-Gauss method. The analysis of the experiments is done using the known theory of solutions to Dirichlet problems for ∆∞(u) = 0, which includes AMLEs (Absolutely Minimizing Lipschitz Extensions), sets of uniqueness, critical segments and lines of singularity. From the experiments one main conjecture is formulated: For Dirichlet problems, which have a non-constant boundary function, it is possible to predict the structure of the lines of singularity in solutions in the Infinity-Laplace case by examining the corresponding Laplace case.