Brokate, Martin Some BV properties of the Preisach hysteresis operator. (English) Zbl 0666.47040 Appl. Anal. 32, No. 3-4, 229-252 (1989). We discuss mapping and Lipschitz continuity properties of the Preisach model for hysteresis in the spaces \(BV[0,1]\) and \(W^{1,1}[0,1]\). Reviewer: M.Brokate Cited in 7 Documents MSC: 47H99 Nonlinear operators and their properties Keywords:Lipschitz continuity properties; Preisach model for hysteresis; Preisach operator; bounded variation PDFBibTeX XMLCite \textit{M. Brokate}, Appl. Anal. 32, No. 3--4, 229--252 (1989; Zbl 0666.47040) Full Text: DOI Link References: [1] Appell J., Expo. Math 6 pp 209– (1988) [2] Brokate M., J. Reine Angew. Math 6 (1988) [3] Honig, C.S. 1975. Volterra Stieltjes - Integral equations. North Holland, Amsterdam. 1975. [4] Krasnosel ’skii M.A., Soviet Math. Dokl 17 pp 447– (1976) [5] Krasnosel ’skii, M.A. and Pokrovskii, A.V. 1983. Systems with hysteresis. Nauka. 1983. [6] Krasnosel ’skii, M.A. 1970.Hysterant operator. Soviet Math. Dokl. 1970. [7] Krej[cbreve], P. The one-dimensional time-periodic case. manuscript. [8] DOI: 10.1007/BF01174335 · Zbl 0658.35065 · doi:10.1007/BF01174335 [9] DOI: 10.1103/PhysRevLett.56.1518 · doi:10.1103/PhysRevLett.56.1518 [10] DOI: 10.1007/BF01349418 · doi:10.1007/BF01349418 [11] Pokrovskii A.V., Soviet Math. Dokl 14 pp 896– (1973) [12] DOI: 10.1016/0362-546X(84)90094-4 · Zbl 0563.35007 · doi:10.1016/0362-546X(84)90094-4 [13] Visintin A., Mathematical models of hysteresis (1988) · Zbl 0656.73043 [14] DOI: 10.1063/1.1735418 · doi:10.1063/1.1735418 [15] Krej[cbreve]i, P. and Lovicar, V. Continuity of hysteresis operators in Sobolev spaces. manuscript. · Zbl 0705.47054 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.