Strongly anisotropic elliptic problems with regular and $L^1$ data

Moussa Chrif; Said El Manouni; Fares Mokhtari

doi:10.4171/pm/1971

JournalspmVol. 72, No. 4pp. 357–391

Strongly anisotropic elliptic problems with regular and $L^{1}$ data

Moussa Chrif
Université Moulay Ismail, Meknès, Morocco
Said El Manouni
Al Imam University (IMSIU), Riyadh, Saudi Arabia
Fares Mokhtari
ENS Kouba, Ecole Supérieure de Commerce, Alger, Algeria

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Abstract

In this paper, we obtain the existence of weak solutions to a class of strongly anisotropic nonlinear elliptic boundary-value problems with nonlinear lower-order term with natural growth in an appropriate anisotropic function space. We investigate the cases where the right hand side term is regular or to be in $L^{1}$ . A uniqueness result is also given in a particular case.

Cite this article

Moussa Chrif, Said El Manouni, Fares Mokhtari, Strongly anisotropic elliptic problems with regular and $L^{1}$ data. Port. Math. 72 (2015), no. 4, pp. 357–391

DOI 10.4171/PM/1971