Work

Elliptic quasivariational-hemivariational inequalities in the Beppo-Levi space

Year: 2026

Type: article

Abstract: In this paper, we study elliptic quasivariational-hemivariational inequalities in the Beppo–Levi space 𝐷 1 , 𝑝 ⁡ ( ℝ 𝑁 ) , where both the constraint set and the associated energy functional depend on the unknown solution. Owing to the lack of compactness of the embedding of 𝐷 1 , 𝑝 ⁡ ( ℝ 𝑁 ) into the standard Lebesgue spaces, we work within an appropriate weighted Lebesgue space framework. To overcome the difficulties arising from the solution-dependent constraints, we introduce an auxiliary penalized problem, whose solvability is established by combining a surjectivity theorem, Minty’s lemma, and Kluge’s fixed-point theorem. Finally, we establish the convergence of penalized solutions and recover a solution of the original quasivariational-hemivariational inequality.

Source: Nonlinear Analysis Real World Applications

DOI: 10.1016/j.nonrwa.2026.104761

Authors: Zijia Peng, Zixian Chen, Xiuwen Li

Institution: Guangxi Minzu University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funder: National Natural Science Foundation of China