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Anisotropic elliptic problems with natural growth terms

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Abstract

In this paper we prove existence and regularity of solutions for nonlinear anisotropic elliptic equations of the type

$$-\sum_{i=1}^N\frac{\partial}{\partial x_i}\left[\left|\frac{\partial u}{\partial {x}_i}\right|^{p_i-2}\frac{\partial u}{\partial x_i}\right]+g(x,u,\nabla u)=f$$

in a bounded, smooth, domain Ω, in \({\mathbb{R}^N}\) , with homogeneous Dirichlet boundary conditions. The right hand side f is assumed to belong to some Lebesgue space and the function g is a nonlinear lower order term.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, 3001-454, Coimbra, Portugal

    Agnese Di Castro

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  1. Agnese Di Castro
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Correspondence to Agnese Di Castro.

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This research supported by CMUC/FCT.

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Di Castro, A. Anisotropic elliptic problems with natural growth terms. manuscripta math. 135, 521–543 (2011). https://doi.org/10.1007/s00229-011-0431-3

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  • DOI: https://doi.org/10.1007/s00229-011-0431-3

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