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Existence and Regularity Results for Some Elliptic Equations with Degenerate Coercivity and Singular Quadratic Lower-Order Terms

  • Rezak SouilahEmail author
Article
  • 45 Downloads

Abstract

In this paper, we study the existence and regularity results for some elliptic equations with degenerate coercivity and singular quadratic lower-order terms with natural growth with respect to the gradient. The model problem is
$$\begin{aligned} \left\{ \begin{array}{ll} - \mathrm {div}\left( \frac{\nabla u}{(1+|u|)^{\gamma }}\right) +\frac{\vert \nabla u\vert ^{2}}{u^{\theta }}=f+u^{r} &{} \quad \text{ in }\ \Omega ,\\ u=0&{} \quad \text{ on }\ \partial \Omega , \end{array}\right. \end{aligned}$$
(0.1)
where \(\Omega \) is a bounded open subset in \(\mathbb {R}^{N}\), \(0<\theta <1\), \(\gamma >0\) and \(0<r<2-\theta \). We will prove existence results for solutions under various assumptions on the summability of the source f.

Keywords

Nonlinear elliptic equations singular quadratic lower-order terms degenerate coercivity 

Mathematics Subject Classification

35J62 35J70 35J75 

Notes

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Authors and Affiliations

  1. 1.Faculté des Sciences Économiques Commerciales et de GestionsUniversité Yahia FaresMédéaAlgeria
  2. 2.Laboratoire d’EDP Non Linéaires et Histoires des Mathématiques ENS-KoubaAlgerAlgeria

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