Regularity results for mixed local and nonlocal double phase functionals (Q6667444)

As mentioned in the primary classification by the authors as `49N60', this paper discusses ``regularity of solutions in optimal control''. There are several areas of research in the field of PDEs. For example, some works investigate new methods for solving them, some works deal with the optimal control of PDEs, and some researches deal with the properties of the solutions. This area in studding PDE is regularity of solutions. The function \(\mathcal{E}\) of the problem under discussion to be minimized is given in a formulation with some necessary conditions. The properties such as the local boundedness, Hölder regularity and Harnack's inequality are studied. Some concepts have been presented for the minimizer of the problem \(u\). These concepts are then proven, which form the main part of the article. Considering the problem under discussion, as a reader, I saw that optimal regularity of solutions was not discussed in the paper or the answer to this question as: what is the optimal regularity of solutions? Those interested in regularity of solutions can read and investigate this article.