Computer-assisted proofs for a nonlinear Laplace-Beltrami equation on the sphere

Séminaire CRM-CAMP Spotlight on Graduate Research (3 déc. 2020 / Dec. 3, 2020)

Gabriel William Duchesne (McGill University, Canada)

Abstract: We prove the existence and local uniqueness of radially symmetric solutions of nonlinear Laplace-Beltrami equation on the sphere by using the Radii Polynomial Theorem on Banach spaces with a combination of Taylor and Chebyshev coefficients of the solutions.