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

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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:
CreatorsEmailORCIDORCID Put Code
Kuehn, MichaelUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
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:
KeywordsLanguage
BOUNDARY-VALUE-PROBLEMS; CONVEX DOMAINS; INFINITY LAPLACIAN; EQUATIONSMultiple languages
Mathematics, Applied; MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/16867

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