Flow-invariant domains of Hölder continuity for nonlinear semigroups
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- by Andrew T. Plant PDF
- Proc. Amer. Math. Soc. 53 (1975), 83-87 Request permission
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 $\lambda = 0$.References
-
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.
D. Brézis, Classes d’interpolation associées à un opérateur monotone, C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A1553-A1556.
M. G. Crandall, A generalized domain for semigroup generators, M.R.C. Technical Report #1189, University of Wisconsin, Madison, Wis.
- 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 287357, DOI 10.2307/2373376
- M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57–94. MR 300166, DOI 10.1007/BF02761448 J. Dieudonné, Fondements de l’analyse moderne, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074.
- Isao Miyadera, Some remarks on semi-groups of nonlinear operators, Tohoku Math. J. (2) 23 (1971), 245–258. MR 296746, DOI 10.2748/tmj/1178242643
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
- G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191–203. MR 0361965, DOI 10.1016/0022-1236(72)90048-1
Additional Information
- © Copyright 1975 American Mathematical Society
- 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