Kuehn, Michael (2018). POWER- AND LOG-CONCAVITY OF VISCOSITY SOLUTIONS TO SOME ELLIPTIC DIRICHLET PROBLEMS. Commun. Pure Appl. Anal, 17 (6). S. 2773 - 2789. SPRINGFIELD: AMER INST MATHEMATICAL SCIENCES-AIMS. ISSN 1553-5258
Full text not available from this repository.Abstract
In this article we consider a special type of degenerate elliptic partial differential equations of second order in convex domains that satisfy the interior sphere condition. We show that any positive viscosity solution u of -|del u|(alpha)Delta(N)(p) u = 1 has the property that u(alpha+1/alpha+2) is a concave function. Secondly we consider positive solutions of the eigenvalue problem -|del u|(alpha)Delta(N)(p) u = lambda|u|(alpha)u, in which case log u turns out to be concave. The methods provided include a weak comparison principle and a Hopf-type Lemma.
Item Type: | Journal Article | ||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-168675 | ||||||||
DOI: | 10.3934/cpaa.2018131 | ||||||||
Journal or Publication Title: | Commun. Pure Appl. Anal | ||||||||
Volume: | 17 | ||||||||
Number: | 6 | ||||||||
Page Range: | S. 2773 - 2789 | ||||||||
Date: | 2018 | ||||||||
Publisher: | AMER INST MATHEMATICAL SCIENCES-AIMS | ||||||||
Place of Publication: | SPRINGFIELD | ||||||||
ISSN: | 1553-5258 | ||||||||
Language: | English | ||||||||
Faculty: | Unspecified | ||||||||
Divisions: | Unspecified | ||||||||
Subjects: | no entry | ||||||||
Uncontrolled Keywords: |
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Refereed: | Yes | ||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/16867 |
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