PreprintPerturbation theory for homogeneous evolution equationsDaniel HauerAbstractIn this paper, we develop a perturbation theory to show that if a homogeneous operator of order \(\alpha\neq1\) is perturbed by a Lipschitz continuous mapping then every mild solution of the firstorder Cauchy problem governed by these operators is strong and the timederivative satisfies a global regularity estimate. We employ this theory to derive global \(L^{q}\)\(L^{\infty}\)estimates of the timederivative of the evolution problem governed by the pLaplaceBeltrami operator and total variational flow operator respectively perturbed by a Lipschitz nonlinearity on a noncompact Riemannian manifold. Keywords: Nonlinearsemigroups,regularityoftimederivative,homogenousop erators, pLaplaceBeltrami operator, total variational flow on manifolds.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/2004.00483.
