PreprintRegularizing effect of homogeneous evolution equations with perturbationDaniel HauerAbstractSince the pioneering work [C. R. Acad. Sci. Paris Sér., 1979] by Aronson & Bénilan and [Johns Hopkins Univ. Press, 1981] by Bénilan & Crandall, it is well-known that first-order evolution problems governed by a nonlinear but homogeneous operator admit the smoothing effect that every corresponding mild solution is Lipschitz continuous for every positive time and if the underlying Banach space has the Radon-Nikodým property, then the mild solution is a.e. differentiable and the time-derivative satisfies global and point-wise bounds.
In this paper, we show that these results remain true if the
homogeneous operator is perturbed by a
Lipschitz continuous mapping. More precisely, we establish point-wise
Aronson–Bénilan type estimates and global
Keywords:
Nonlinear semigroups, Aronson-Bénilan estimates, regularity of time-derivative,
homogenous operators, AMS Subject Classification: Primary 47H20; secondary 47h06, 47H14, 47J35, 35B65. This paper is available as a pdf (324kB) file. It is also on the arXiv: arxiv.org/abs/2004.00483v2.
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