Special Session 110: Evolution Equations with Applications to Control, Mathematical Modeling and Mechanics

A priori estimates for anisotropic systems

Maria-Magdalena Boureanu
University of Craiova, Romania
Romania
Co-Author(s):    Alejandro Velez-Santiago
Abstract:
We study anisotropic systems with variable exponents involving Leray-Lions type operators not only in the interior of the domain, but also on the boundary. To justify the study of such general systems, we provide multiple examples of operators satisfying our hypotheses. Our goal is to deduce the existence, the uniqueness, and the global regularity of the weak solution. All these results were recently obtained in a joint work with Alejandro V\`elez\,-\,Santiago.