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Abstract

We consider the p-Laplacian in \(\mathbb {R}^d\) perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for \(p>d \) and \(p=d\) and discuss the connection with Sobolev interpolation inequalities.

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Acknowledgments

Financial support through Swedish research council grant FS-2009-493 (T. E.), US National Science Foundation grant PHY-1347399 (R. F.) and grant MIUR-PRIN08 grant for the project “Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni” (H. K.) is acknowledged.

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Correspondence to Rupert L. Frank.

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Communicated by L. Ambrosio.

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Ekholm, T., Frank, R.L. & Kovařík, H. Weak perturbations of the p-Laplacian. Calc. Var. 53, 781–801 (2015). https://doi.org/10.1007/s00526-014-0767-0

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