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Publication - Dr Ivor McGillivray

    An isoperimetric inequality in the plane with a log-convex density

    Citation

    McGillivray, I, 2018, ‘An isoperimetric inequality in the plane with a log-convex density’. Ricerche di Matematica., pp. 1-58

    Abstract

    Given a positive lower semi-continuous density f on (Formula presented.) the weighted volume (Formula presented.) is defined on the (Formula presented.)-measurable sets in (Formula presented.). The f-weighted perimeter of a set of finite perimeter E in (Formula presented.) is written (Formula presented.). We study minimisers for the weighted isoperimetric problem (Formula presented.)for (Formula presented.). Suppose f takes the form (Formula presented.) where (Formula presented.) is a non-decreasing convex function. Let (Formula presented.) and B a centred ball in (Formula presented.) with (Formula presented.). We show that B is a minimiser for the above variational problem and obtain a uniqueness result.

    Full details in the University publications repository