On Lp -viscosity solutions of bilateral obstacle problems with unbounded ingredients

Shigeaki Koike, Shota Tateyama

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Abstract

The global equi-continuity estimate on Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of Lp-viscosity solutions is established via an approximation of given data. The local Hölder continuity estimate on the first derivative of Lp-viscosity solutions is shown when the obstacles belong to C1,β, and p> n.

Original languageEnglish
JournalMathematische Annalen
DOIs
Publication statusPublished - 2019 Jan 1

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ASJC Scopus subject areas

  • Mathematics(all)

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