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PDF-Sep.26ThePerronMethodInthislectureweshowthatonecanshowexistenceofsolut PDF document

iiLetvbesubharmonicinnifthereisx02nwithvx0supnvxthenvisconstantInparticularifv2C0nthenvx6maxnvyforallx2niiiIfv1vkaresubharmonicsoisvmaxfv1vkgProofiItisclearthatv6

ii.Letvbesubharmonicin\n ifthereisx02\nwithv(x0)=sup\nv(x) thenvisconstant.Inpartic-ular ifv2C0(\n) thenv(x)6max@\nv(y)forallx2\n.iii.Ifv1;;vkaresubharmonic soisvmaxfv1;;vkg.Proof.i.Itisclearthatv6

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