The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Interfaces and Free Boundaries

Full-Text PDF (614 KB) | Metadata | Table of Contents | IFB summary
Volume 17, Issue 1, 2015, pp. 93–115
DOI: 10.4171/IFB/335

Published online: 2015-05-26

On regularity properties of solutions to the hysteresis-type problem

Darya E. Apushkinskaya[1] and Nina N. Uraltseva[2]

(1) Universität des Saarlandes, Saarbrücken, Germany
(2) St. Petersburg State University, Russian Federation

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 $W^{2,1}_q$ with sufficiently large $q$ and prove that in fact $q = \infty$. In other words, we establish the optimal regularity of solutions. Our arguments are based on quadratic growth estimates for solutions near the free boundary.

Keywords: Free boundary, hysteresis, sub-caloric functions, monotonicity formula, quadratic growth estimates

Apushkinskaya Darya, Uraltseva Nina: On regularity properties of solutions to the hysteresis-type problem. Interfaces Free Bound. 17 (2015), 93-115. doi: 10.4171/IFB/335