This paper develops Freud-Sobolev orthogonal polynomials, proves quantitative compactness estimates for the H^1(e^{-V}) embedding, and uses computer-assisted proofs to enclose solutions of the sextic Gross-Pitaevskii equation.
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Numerical Analysis of differential equations on weighted Sobolev spaces: beyond classical orthogonal polynomials
This paper develops Freud-Sobolev orthogonal polynomials, proves quantitative compactness estimates for the H^1(e^{-V}) embedding, and uses computer-assisted proofs to enclose solutions of the sextic Gross-Pitaevskii equation.