The obstacle problem for noncoercive elliptic equations with variable growth and $L^1$-data

Hocine Ayadi; Fares Mokhtari; Rezak Souilah

doi:10.4171/pm/2079

JournalspmVol. 79, No. 1/2pp. 61–83

The obstacle problem for noncoercive elliptic equations with variable growth and $L^{1}$ -data

Hocine Ayadi
University of Medea, Algeria
Fares Mokhtari
University of Algiers, Algeria
Rezak Souilah
University of Medea, Algeria

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Abstract

The aim of this paper is to study the obstacle problem associated with noncoercive elliptic equations with variable exponents and $L^{1}$ -data. After proving the existence and regularity of entropy solutions, we have extended the Lewy–Stampacchia inequalities to the case of noncoercive elliptic operators.

Cite this article

Hocine Ayadi, Fares Mokhtari, Rezak Souilah, The obstacle problem for noncoercive elliptic equations with variable growth and $L^{1}$ -data. Port. Math. 79 (2022), no. 1/2, pp. 61–83

DOI 10.4171/PM/2079