Graph properties for nonlocal minimal surfaces

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    Abstract

    © 2016, Springer-Verlag Berlin Heidelberg. In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension 3, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler–Lagrange equation related to the nonlocal mean curvature.
    Original languageEnglish
    JournalCalculus of Variations and Partial Differential Equations
    Volume55
    Issue number4
    DOIs
    Publication statusPublished - 2016

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