Abstract:<abstract><p>We define rigorously a solution to the fourth-order total variation flow equation in $ \mathbb{R}^n $. If $ n\geq3 $, it can be understood as a gradient flow of the total variation energy in $ D^{-1} $, the dual space of $ D^1_0 $, which is the completion of the space of compactly supported smooth functions in the Dirichlet norm. However, in the low dimensional case $ n\leq2 $, the space $ D^{-1} $ does not contain characteristic functions of sets of positive measure, so we extend the … Show more
<abstract><p>This contribution is the preface of the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday.</p></abstract>
<abstract><p>This contribution is the preface of the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday.</p></abstract>
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