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[see pdf for notation]-Reularity for the Solution of Strongly Nonlinear Eigenvalue Problems on Orlicz-Sobolev Spaces

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[see pdf for notation]-Reularity for the Solution of Strongly Nonlinear Eigenvalue Problems on Orlicz-Sobolev Spaces

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dc.contributor.author Vuillermot, Pierre A. en
dc.date.accessioned 2010-06-09T15:29:58Z en
dc.date.available 2010-06-09T15:29:58Z en
dc.date.issued 1984-08 en
dc.identifier.uri http://hdl.handle.net/10106/2441 en
dc.description.abstract We present a new method to prove the [see pdf for notation]-regularity of the eigenfunctions for Dirichlet problems with strictly convex Young functionnonlinearities in their principal part. The basic idea is threefold: we first invoke the topological methods of [12] to infer the existence of a countable infinity of [see pdf for notation]-eigensolutions; we then use Schauder's inversion technique to associate with each one of these eigensolutions a unique [see pdf for notation]-solution of an auxiliary Dirichlet problem; we finally prove the [see pdf for notation]-regularity of the original elgensolutions from the [see pdf for notation]-regularity of the auxiliary solutions, using distributional arguments and a new convexity inequality which characterizes the shape of the given nonlinearities. We give several examples and counter examples which illustrate the role of the various hypotheses, and which allow comparison with Pohozaev's celebrated existence and non-existence results [4]. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;218 en
dc.subject Nonlinear eigenvalue problems en
dc.subject Convexity inequality for Young functions en
dc.subject Regularity theory on Orlicz-Sobolev spaces en
dc.subject Orlicz-Sobolev en
dc.subject Dirichlet problem en
dc.subject.lcsh Mathematics Research en
dc.title [see pdf for notation]-Reularity for the Solution of Strongly Nonlinear Eigenvalue Problems on Orlicz-Sobolev Spaces en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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