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Infinity Laplacian equations with singular absorptions

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Abstract

In this work, we study regularity properties for nonvariational singular elliptic equations ruled by the infinity Laplacian. We obtain optimal \(C^{1,\alpha }\) regularity along the free boundary. We also show existence of solutions, nondegeneracy properties and fine geometric estimates for the free boundary.

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Acknowledgements

The authors would like to thank the anonymous referee for the careful and detailed reading and for your valuable suggestions and corrections. This paper is part of the second author’s Ph.D. thesis. GSS acknowledges support from CAPES-Brazil and would like to thank the Department of Mathematics at Universidade Federal da Paraíba for the pleasant and productive period during his Ph.D. program at that institution. DJA thanks the Abdus Salam International Centre for Theoretical Physics (ICTP) for the great hospitality during his research visits. DJA and GSS are partially supported by CNPq and grant 2019/0014 Paraíba State Research Foundation (FAPESQ).

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Authors and Affiliations

  1. UFPB, Department of Mathematics, Universidade Federal da Paraíba, 58059-900, João Pessoa, PB, Brazil

    Damião J. Araújo & Ginaldo S. Sá

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  1. Damião J. Araújo
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  2. Ginaldo S. Sá
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Correspondence to Damião J. Araújo.

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Communicated by O. Savin.

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Araújo, D.J., Sá, G.S. Infinity Laplacian equations with singular absorptions. Calc. Var. 61, 132 (2022). https://doi.org/10.1007/s00526-022-02241-4

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