We consider the equation −Δw=w3 with zero boundary conditions on planar domains that are conformal images of annuli. Starting with an approximate solution, we prove that there exists a true solution nearby. Our approach is computer-assisted. It involves simultaneous and accurate control of the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.
Validated numerical solutions for a semilinear elliptic equation on some topological annuli in the plane
Arioli, Gianni;
2023-01-01
Abstract
We consider the equation −Δw=w3 with zero boundary conditions on planar domains that are conformal images of annuli. Starting with an approximate solution, we prove that there exists a true solution nearby. Our approach is computer-assisted. It involves simultaneous and accurate control of the (inverse) Dirichlet Laplacean, nonlinearities, and conformal mappings.File in questo prodotto:
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