On regularity properties of solutions to hysteresis-type problems.
Seminar Room 2, Newton Institute Gatehouse
AbstractWe 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. The main feature of this problem is that the operator at the right-hand side is a multivalued. We present some results concerning the optimal regularity of solutions. Our arguments are based on quadratic growth estimates for solutions near the free boundary. The talk is based on joint work with Nina Uraltseva.
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