Existence and regularity of solutions for elliptic systems with mixed boundary conditions

In this article we study elliptic systems involving nonstandard mixed boundary conditions in a bounded domain, possibly multiply connected. We prove the existence and uniqueness of weak and strong solutions of such problems in the Hilbert setting. Then, we generalize our results to the \(L^p\)-theory using some inf-sup conditions. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/103/abstr.html