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  4. Degenerate elliptic problem with singular gradient lower order term and variable exponents

Degenerate elliptic problem with singular gradient lower order term and variable exponents

MMC.
2023;
Volume 10, Number 1
: pp. 133–146
https://doi.org/10.23939/mmc2023.01.133
Received: April 01, 2022
Revised: October 10, 2022
Accepted: October 17, 2022

Mathematical Modeling and Computing, Vol. 10, No. 1, pp. 133–146 (2023)

Authors:
  1. M. A. Zouatini
  2. F. Mokhtari
  3. H. Khelifi
1
Department of Mathematics, Faculty of Sciences, University of Algiers, Algiers, Algeria; Laboratory LEDPNL, HM, ENS-Kouba, Algiers, Algeria
2
Department of Mathematics, Faculty of Sciences, University of Algiers, Algiers, Algeria; Laboratory of Mathematical Analysis and Applications, University of Algiers 1, Algiers, Algeria
3
Department of Mathematics, Faculty of Sciences, University of Algiers, Algiers, Algeria; Laboratory LEDPNL, HM, ENS-Kouba, Algiers, Algeria

In this paper, we prove the existence and regularity of weak solutions for a class of nonlinear elliptic equations with degenerate coercivity and singular lower-order terms with natural growth with respect to the gradient and $L^{m(\cdot)}$ ($m(x)\geq 1$) data.  The functional setting involves Lebesgue–Sobolev spaces with variable exponents.

degenerate problem
singular term
regularity solution
the comparison principle
Harnack inequality
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