2024-03-29T05:22:35Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698692022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equationsHAMAMUKI, NAOHarnack inequalityFully nonlinear elliptic equationsDiscrete solutionsViscosity solutions410We present a new Harnack inequality for non-negative discrete supersolutions of fully nonlinear uniformly elliptic difference equations on rectangular lattices. This estimate applies to all supersolutions; instead the Harnack constant depends on the graph distance on lattices. For the proof we modify the proof of the weak Harnack inequality. Applying the same idea to elliptic equations in a Euclidean space, we also derive a Harnack type inequality for non-negative viscosity supersolutions.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69869info:doi/10.14943/84209https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69869/1/pre1065.pdfHokkaido University Preprint Series in Mathematics10651162015-02-23engpublisher