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Flow-invariant domains of Hölder continuity for nonlinear semigroups


Author: Andrew T. Plant
Journal: Proc. Amer. Math. Soc. 53 (1975), 83-87
MSC: Primary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1975-0377611-0
MathSciNet review: 0377611
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Abstract: Let $ S(t)$ be a nonlinear semigroup, on Banach space $ X$, generated by an accretive set $ A$. The set of $ x$ in $ X$ such that $ t \to S(t)x$ is Hölder continuous, with Hölder exponent $ \sigma \,\epsilon \,(0,\;1]$, is flow-invariant and is characterised by the behaviour of the map $ \lambda \to {(I + \lambda A)^{ - 1}}x$ at $ \lambda = 0$.


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  • [1] Ph. Bénilan, Solutions intégrates d'equations d'évolution dans un espace de Banach, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A47-A50. MR 45 #9212.
  • [2] D. Brézis, Classes d'interpolation associées à un opérateur monotone, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1553-A1556.
  • [3] M. G. Crandall, A generalized domain for semigroup generators, M.R.C. Technical Report #1189, University of Wisconsin, Madison, Wis.
  • [4] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265–298. MR 0287357, https://doi.org/10.2307/2373376
  • [5] M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57–94. MR 0300166, https://doi.org/10.1007/BF02761448
  • [6] J. Dieudonné, Fondements de l'analyse moderne, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074.
  • [7] Isao Miyadera, Some remarks on semi-groups of nonlinear operators, Tôhoku Math. J. (2) 23 (1971), 245–258. MR 0296746, https://doi.org/10.2748/tmj/1178242643
  • [8] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
  • [9] G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191–203. MR 0361965

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0377611-0
Keywords: Banach space, nonlinear semigroup, accretive set, flow-invariant, Hölder continuous
Article copyright: © Copyright 1975 American Mathematical Society

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