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Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations

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Title: Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations
Authors: HAMAMUKI, NAO Browse this author
Keywords: Harnack inequality
Fully nonlinear elliptic equations
Discrete solutions
Viscosity solutions
Issue Date: 23-Feb-2015
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1065
Start Page: 1
End Page: 16
Abstract: We 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69869
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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