Existence of solutions for nonlinear elliptic variational inequalities with L¹ data

Abstract

This article addresses the regularizing effect of the interaction between the coefficient of the zero-order term and the datum f in some elliptic variational inequalities. Even if the datum f only belongs to $L^1$, the existence of bounded weak solutions to such problems are proven. This generalizes, to some extent, the previous results in the literature.

Keywords:

• Nonlinear elliptic variational inequalities
• variable exponents
• $L^1$ data
• bounded weak solutions

AMS Subject Classifications:

• 35J87
• 47J20
• 35A01

Acknowledgments

The authors would like to thank the referees for a careful reading of the manuscript and valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China(grant number 11801259, 11461048), the Natural Science Foundation of Jiangxi Province (grant number 20202BABL201009) and the foundation of Education Department of Jiangxi Province(grant numbers GJJ170604, GJJ190514).