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On the viscosity solutions to Trudinger’s equation

  • Tilak Bhattacharya
  • Leonardo MarazziEmail author
Article

Abstract

We study the existence of positive viscosity solutions to Trudinger’s equation for cylindrical domains \({\Omega\times[0, T)}\), where \({\Omega\subset {I\!R}^{n}, n\ge 2,}\) is a bounded domain, T > 0 and \({2\le p < \infty}\). We show existence for general domains \({\Omega,}\) when \({n<p<\infty}\). For \({2\le p\le n}\), we prove existence for domains \({\Omega}\) that satisfy a uniform outer ball condition. We achieve this by constructing suitable sub-solutions and super-solutions and applying Perron’s method.

Mathematics Subject Classification

35K65 35K55 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsWestern Kentucky UniversityBowling GreenUSA
  2. 2.Department of Liberal ArtsSavannah College of Arts and DesignSavannahUSA

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