Besov regularity and optimal estimation of bilevel variational inequality problems on cylindrical domains and their applications.

In this paper, we provide a unified approach to investigating Besov regularity and the optimum estimate for bilevel variational inequality problems on cylindrical domains. This method is effective even with limited summary data available, demonstrating its practicality. The novelty of our approach resides in the treatment of subquadratic growth conditions associated with the gradient variable. We extend our exploration to more challenging geometric configurations, such as a cylinder with a rough base. These configurations introduce novel challenges arising from lateral boundary conditions—an aspect yet unaddressed in prior literature. Further enhancing the relevancy of our approach, we explore its practical applications by establishing higher differentiability results for solutions to the aforementioned problem. Importantly, these results are established under nonlocal conditions that factor in the disparity between the growth and the ellipticity exponents [ABSTRACT FROM AUTHOR]