- 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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