WIAS Preprint No. 2628, (2019)

Variable step mollifiers and applications


  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Papafitsoros, Kostas
    ORCID: 0000-0001-9691-4576
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296

2010 Mathematics Subject Classification

  • 46E35 42B20 49J40 26A45


  • Mollification, integral operators, boundary values, density of convex sets




We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of the operator in all basic Lebesgue, Sobolev and BV spaces as well as corresponding approximation results. The results are then applied to extend recently developed theory concerning the density of convex intersections.

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