J. Evol. Equ. 18 (2018), 1595–1632 © 2018 Springer International Publishing AG, part of Springer Nature Journal of Evolution 1424-3199/18/041595-38, published online May 29, 2018 Equations https://doi.org/10.1007/s00028-018-0453-3 The Yamabe ﬂow on incomplete manifolds Yuanzhen Shao Abstract. This article is concerned with developing an analytic theory for second-order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an L -framework are established by maximal regularity tools. These techniques are applied to the Yamabe ﬂow. It is proven that the Yamabe ﬂow admits a unique local solution within a class of incomplete initial metrics. 1. Introduction Nowadays, there is a rising interest in the study of differential operators on mani- folds with singularities, which is motivated by a variety of applications from applied mathematics, geometry and topology. All the work is more or less related to the semi- nal paper by Kondrat’ev . Among the tremendous amount of the literature on this topic, I would like to mention two lines of research on the study of differential oper- ators of Fuchs type, which have been introduced independently by Melrose [36,37], Nazaikinskii et al. , Schulze [45,46] and Schulze and Seiler . One important direction of research on singular
Journal of Evolution Equations – Springer Journals
Published: May 29, 2018
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