Weak solutions for a stochastic mean curvature flow of two-dimensional\n graphs

2014/12/18 by Martina Hofmanová, Hofmanova, Martina, Matthias Roeger +3 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1412.5863

openalex publication_date 2014/12/18 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We study a stochastically perturbed mean curvature flow for graphs in\n\ℝ³ over the two-dimensional unit-cube subject to periodic boundary\nconditions. In particular, we establish the existence of a weak martingale\nsolution. The proof is based on energy methods and therefore presents an\nalternative to the stochastic viscosity solution approach. To overcome\ndifficulties induced by the degeneracy of the mean curvature operator and the\nmultiplicative gradient noise present in the model we employ a three step\napproximation scheme together with refined stochastic compactness and\nmartingale identification methods.\n

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