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null Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Maso, Gianni / Benedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Manfredi, Juan / McCann, Robert / Mingione, Giuseppe / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Kristensen, Jan
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1Department of Mathematics and Computer Science, Western Kentucky University, Bowling Green, KY 42101, USA.
2Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA.
Citation Information: Advances in Calculus of Variations. Volume 4, Issue 4, Pages 445–487, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: 10.1515/acv.2010.019, February 2011
Publication History:
Under appropriate conditions on ƒ(x, t), we prove the existence of viscosity solutions to Δ∞ u = ƒ(x, u) that take prescribed continuous data on the boundary of bounded domains. As an application, singular boundary value problems are investigated. These problems are shown to admit viscosity solutions and their asymptotic behavior near the boundary is analyzed. Maximum and comparison principles are used as the main tools in these investigations.
Keywords.: Infinity-Laplacian; comparison principle; Dirichlet problems; singular boundary value problem
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