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Large solutions for the elliptic 1-Laplacian with absorption

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Abstract

In this paper, we give a general condition on the absorption term of the 1-Laplace elliptic equation for the existence of suitable large solutions. This condition can be considered as the corresponding Keller-Osserman condition for the p-Laplacian, in the case p = 1. We also provide conditions that guarantee uniqueness of solutions to such problems.

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Authors and Affiliations

  1. Departament d’Anàlisi Matemàtica, Universitat de València, Valencia, Spain

    Salvador Moll

  2. Dipartimento S.B.A.I Sapienza, Università di Roma, Roma, Italy

    Francesco Petitta

Authors
  1. Salvador Moll
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  2. Francesco Petitta
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Corresponding author

Correspondence to Francesco Petitta.

Additional information

S. M. was partially supported by project MTM2012-31103.

F. P. was partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Moll, S., Petitta, F. Large solutions for the elliptic 1-Laplacian with absorption. JAMA 125, 113–138 (2015). https://doi.org/10.1007/s11854-015-0004-6

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  • DOI: https://doi.org/10.1007/s11854-015-0004-6

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