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Estimates for solutions to nonlinear degenerate elliptic equations with lower order terms

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Abstract

We consider a class of Dirichlet boundary problems for nonlinear degenerate elliptic equations with lower order terms. We prove, using symmetrization techniques, pointwise estimates for the rearrangement of the gradient of a solution u and integral estimates. As consequence, we get apriori estimates which show how the summability of the gradient of a solution increases when the summability of the datum increases, also taking into account the presence of a zero order term which can have a regularizing effect.

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Acknowledgements

The authors are members of 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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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi di Napoli Parthenope, Centro Direzionale, Isola C4, 80143, Naples, Italy

    Maria Francesca Betta & Gabriella Paderni

  2. Dipartimento di Matematica e Fisica, Università degli Studi della Campania, Viale Lincoln 5, 81100, Caserta, Italy

    Adele Ferone

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  1. Maria Francesca Betta
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  2. Adele Ferone
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  3. Gabriella Paderni
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Correspondence to Maria Francesca Betta.

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Betta, M.F., Ferone, A. & Paderni, G. Estimates for solutions to nonlinear degenerate elliptic equations with lower order terms. Ricerche mat 69, 367–384 (2020). https://doi.org/10.1007/s11587-019-00467-7

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