A novel finite element method provides the first explicit two-sided eigenvalue bounds for Schrödinger operators with singular potentials on unbounded domains, demonstrated on hydrogen and H2+ systems.
Talenti, Best constant in Sobolev inequality,Ann
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Proves relative compactness in the energy space for bounded sequences solving subcritical mixed local-nonlocal problems with exponents approaching 2*, under specific ranges of N and p, yielding infinitely many sign-changing solutions to the critical equation.
Sharp quantitative stability is proved for the affine fractional L2-Sobolev inequality, identifying the affine Hessian kernel and showing the global stability constant is strictly smaller than the local spectral gap.
For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.
citing papers explorer
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Explicit Two-Sided Eigenvalue Bounds for Schr\"odinger Operators with Singular Potentials via Finite Element Method
A novel finite element method provides the first explicit two-sided eigenvalue bounds for Schrödinger operators with singular potentials on unbounded domains, demonstrated on hydrogen and H2+ systems.
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Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
Proves relative compactness in the energy space for bounded sequences solving subcritical mixed local-nonlocal problems with exponents approaching 2*, under specific ranges of N and p, yielding infinitely many sign-changing solutions to the critical equation.
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Sharp Stability for the Affine Fractional Sobolev Inequality
Sharp quantitative stability is proved for the affine fractional L2-Sobolev inequality, identifying the affine Hessian kernel and showing the global stability constant is strictly smaller than the local spectral gap.
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A note on the Sobolev--Escobar bridge inequality
For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.