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Multi-valued solutions to Hessian equations

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Abstract

In this paper, we use the Perron method to prove the existence of bounded multi-valued viscosity solutions to Hessian equations and interior Lipschitz continuity of the multi-valued solutions.

Mathematics Subject Classification (2000)

35J60 

Keywords

Hessian equations Multi-valued solutions Viscosity solutions Existence 
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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceWeifang UniversityShandongPeople’s Republic of China
  2. 2.School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of EducationBeijingPeople’s Republic of China

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