22-55 Gianni Arioli, Hans Koch
Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane (6421K, pdf) Oct 6, 22
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Abstract. We consider the equation -Laplace w = w^3 with zero boundary conditions on planar domains that are conformal images of annuli. Starting with an approximate solution, we prove that there exist a true solution nearby. Our approach is computer-assisted. It involves simultaneous and accurate control of the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.

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