Entropy solutions for nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity

ABSTRACT

This article is devoted to the study of a class of nonlinear anisotropic elliptic equations with degenerate coercivity, lower order term and $L^1$ datum in appropriate anisotropic variable exponent Sobolev space. We obtain the existence of the entropy solutions via strong convergence of the truncations and we derive some properties of these solutions.

COMMUNICATED BY:

• L. Diening

KEYWORDS:

• Anisotropic elliptic equations
• variable exponents
• degenerate coercivity
• entropy solutions
• $L^1$ data

AMS SUBJECT CLASSIFICATIONS:

• 35J70
• 35J60
• 35B65
• 35B45

Acknowledgments

The authors would like to thank the referees for the useful comments and suggestions that substantially helped improving the quality of the paper. They are also very grateful to Pr. Jean-Michel Rakotoson for his helpful advice and discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hocine Ayadi  http://orcid.org/0000-0002-0131-4437

Additional information

Funding

Hocine Ayadi is partially supported by the Algerian Ministry of Higher Education and Scientific Research under the PRFU Project [C00L03UN280120180004].