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Sobolev–Zygmund solutions for nonlinear elliptic equations with growth coefficients in BMO

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Abstract

In this paper we study, in the setting of the Zygmund–Sobolev spaces, weak solutions to Dirichlet problems for nonlinear elliptic equations in divergence form with unbounded coefficients of the type

$$\begin{aligned} {\text {div}}\;({\mathcal {A}}(x,\nabla u)+{\mathcal {B}}(x,u)) = {\text {div}}\;{\mathcal {F}} \end{aligned}$$

in a bounded Lipschitz domain \(\Omega \subset {{\mathbb {R}}}^{N}\), \(N>2\).

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Funding

This study was funded by ‘Indam-Gnampa’—Istituto Nazionale Alta Matematica - Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II, 84084, Fisciano, SA, Italy

    Patrizia Di Gironimo

  2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia, 80126, Naples, Italy

    Gabriella Zecca

Authors
  1. Patrizia Di Gironimo
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  2. Gabriella Zecca
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Correspondence to Gabriella Zecca.

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Patrizia Di Gironimo declares that she has no conflict of interest. Gabriella Zecca declares that she has no conflict of interest.

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Di Gironimo, P., Zecca, G. Sobolev–Zygmund solutions for nonlinear elliptic equations with growth coefficients in BMO. J Elliptic Parabol Equ 6, 507–527 (2020). https://doi.org/10.1007/s41808-020-00064-y

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  • DOI: https://doi.org/10.1007/s41808-020-00064-y

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