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Harnack inequalities for supersolutions of fully nonlinear elliptic difference and differential equations
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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