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\(p-\)Harmonic Functions in the Upper Half-space

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Abstract

This paper investigates the existence, nonexistence, and qualitative properties of p-harmonic functions in the upper half-space \(\mathbb {R}^N_+\) \((N\ge 3)\) satisfying nonlinear boundary conditions for \(1<p<N\). Moreover, the symmetry of positive solutions is shown by using the method of moving planes.

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Funding

J.M. do Ó acknowledges partial support from CNPq through grants 312340/2021-4 and 429285/2016-7 and Paraíba State Research Foundation (FAPESQ), grant no 3034/2021. E. Medeiros acknowledges partial support from CNPq through grant 308900/2019-7. R. Clemente acknowledges partial support from CNPq through grant 304454/2022-2

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, 30161-970, Brazil

    E. Abreu

  2. Department of Mathematics, Rural Federal University of Pernambuco, Recife, Pernambuco, 52171-900, Brazil

    R. Clemente

  3. Department of Mathematics, Federal University of Paraíba, João Pessoa, Paraíba, 58051-900, Brazil

    J. M. do Ó & E. Medeiros

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  1. E. Abreu
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  2. R. Clemente
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  3. J. M. do Ó
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  4. E. Medeiros
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all authors. The authors read and approved the final manuscript

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Correspondence to J. M. do Ó.

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Abreu, E., Clemente, R., do Ó, J.M. et al. \(p-\)Harmonic Functions in the Upper Half-space. Potential Anal 60, 1383–1406 (2024). https://doi.org/10.1007/s11118-023-10092-7

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