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Singular solutions to conformal Hessian equations

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Abstract

The authors show that for any ε ∈]0, 1[, there exists an analytic outside zero solution to a uniformly elliptic conformal Hessian equation in a ball B ⊂ ℝ5 which belongs to C 1,ε(B) \C 1,ε+(B).

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Acknowledgments

The authors are deeply grateful to the anonimous referee whose advise permitted to ameliorate significantly our exposition.

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Authors and Affiliations

  1. Aix Marseille Université, CNRS, Centrale Marseille, I2M UMR 7373, 13453, Marseille, France

    Nikolai Nadirashvili & Serge Vlăduţ

  2. IITP RAS, B. Karetnyi, 9, Moscow, Russia

    Serge Vlăduţ

Authors
  1. Nikolai Nadirashvili
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  2. Serge Vlăduţ
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Corresponding author

Correspondence to Nikolai Nadirashvili.

Additional information

Dedicated to Professor Haim Brezis on the occasion of his 70th birthday

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Nadirashvili, N., Vlăduţ, S. Singular solutions to conformal Hessian equations. Chin. Ann. Math. Ser. B 38, 591–600 (2017). https://doi.org/10.1007/s11401-017-1085-6

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  • DOI: https://doi.org/10.1007/s11401-017-1085-6

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