Harnack inequality for quasiiinear elliptic equations on Riemannian manifoldsHarnack inequality for quasilinear elliptic equations on Riemannian manifolds
- Other Titles
- Harnack inequality for quasilinear elliptic equations on Riemannian manifolds
- Authors
- Kim, Soojung
- Issue Date
- Feb-2018
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.264, no.3, pp.1613 - 1660
- Journal Title
- JOURNAL OF DIFFERENTIAL EQUATIONS
- Volume
- 264
- Number
- 3
- Start Page
- 1613
- End Page
- 1660
- URI
- http://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/39245
- DOI
- 10.1016/j.jde.2017.10.003
- ISSN
- 0022-0396
- Abstract
- We study viscosity solutions to degenerate and singular elliptic equations L-F vertical bar u vertical bar : = div(F'(del vertical bar del u vertical bar)/vertical bar del u vertical bar u) = h of p-Laplacian type on Riemannian manifolds, where an even function F is an element of C-1 (R) boolean AND C-2 (0, infinity) is supposed to be strictly convex on (0, infinity). Under the assumption that either F is an element of C-2 (R) or its convex conjugate F* is an element of C-2 (R) with some structural condition, we establish a (locally) uniform ABP type estimate and the Krylov-Safonov type Harnack inequality on Riemannian manifolds with the use of an intrinsic geometric quantity to the operator. Here, the C-2-regularities of F and F* account for degenerate and singular operators, respectively. (c) 2017 Elsevier Inc. All rights reserved.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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