On regularity properties of solutions to the hysteresis-type problems
arXiv:1410.6719 · doi:10.4171/IFB/335
Abstract
We consider equations with the simplest hysteresis operator at the right-hand side. Such equations describe the so-called processes "with memory" in which various substances interact according to the hysteresis law. We restrict our consideration on the so-called "strong solutions" belonging to the Sobolev class with sufficiently large and prove that in fact . In other words, we establish the optimal regularity of solutions. Our arguments are based on quadratic growth estimates for solutions near the free boundary.