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  • Titel
    Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphs
  • Verfasser
    Dabrock, Nils ; Hofmanová, Martina ; Röger, Matthias
  • Enthalten in
    Probability Theory and Related Fields, Jg. 179, S. 407-449
  • Erschienen
    2021
  • Sprache
    Englisch
  • Dokumenttyp
    Aufsatz in einer Zeitschrift
  • URN
    urn:nbn:de:0070-pub-29374714 
  • DOI
    10.1007/s00440-020-01012-6 
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Abstract
  • We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. For the first time, we are able to construct martingale solutions which satisfy the equation pointwise and not only in a generalized (distributional or viscosity) sense. Moreover, we study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an L-w,x,t(infinity) estimate for the gradient and an L-w, x,t(2) bound for the Hessian. The proof makes essential use of the delicate interplay between the deterministic mean curvature part and the stochastic perturbation, which permits to show that certain gradient-dependent energies are supermartingales. Our energy bounds in particular imply that solutions become asymptotically spatially homogeneous and approach a Brownian motion perturbed by a random constant.
Inhalt
Statistik
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