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Creators/Authors contains: "Smits, Robert"

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  1. ; ; (, Nonlinear Analysis)
    We establish rigorous quantitative inequalities for the first eigenvalue of the generalized š¯‘¯-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter š¯›¼ is positive, and the superconducting generation regime (š¯›¼ < 0), where the boundary acts as a source. In bounded domains, we use a unified approach to derive a precise asymptotic behavior for all š¯‘¯ and all small real š¯›¼, improving existing results in various directions, including requiring weaker boundary regularity for the case of the classical 2-Robin problem, studied in the fundamental work by RenĆ© Sperb. In exterior domains, we characterize the existence of eigenvalues, establish general inequalities and asymptotics as š¯›¼ ā†’ 0 for the first eigenvalue of the exterior of a ball, and obtain some sharp geometric inequalities for convex domains in two dimensions. 
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    Free, publicly-accessible full text available January 1, 2027
  2. ; ; ; ; ; ; ; (, The Journal of Geometric Analysis)
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