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Nonlinear problems with unbounded coefficients and \(L^1\) data

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Abstract

We consider a class of nonlinear elliptic problems whose prototype involves a coefficients matrix blowing up for a finite value m of the unknown u. Since datum is in \(L^1\), a suitable notion of renormalized solutions is introduced taking into account that u can reach the value m and the existence of such solutions is proved. We study the corresponding evolution problem as well.

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Acknowledgements

This work has been partially supported by FFARB and has partially done during the visits of the first author to Laboratoire de Mathématiques “Raphaël Salem” de l’Université de Rouen. Hospitality and support of this institution is gratefully acknowledged.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi di Napoli “Parthenope”, Isola C4 Centro Direzionale, 80100, Napoli, Italy

    Filomena Feo

  2. Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie, 76801, Saint Etienne du Rouvray Cedex, France

    Olivier Guibé

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  1. Filomena Feo
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  2. Olivier Guibé
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Correspondence to Filomena Feo.

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Feo, F., Guibé, O. Nonlinear problems with unbounded coefficients and \(L^1\) data. Nonlinear Differ. Equ. Appl. 27, 49 (2020). https://doi.org/10.1007/s00030-020-00652-w

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  • DOI: https://doi.org/10.1007/s00030-020-00652-w

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