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Mediterranean Journal of Mathematics

, Volume 9, Issue 1, pp 1–20 | Cite as

Conformal Killing Vector Fields and Rellich Type Identities on Riemannian Manifolds, II

  • Yuri Bozhkov
  • Enzo Mitidieri
Article

Abstract

We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators.

Mathematics Subject Classification (2010)

35J50 35J20 35J60 

Keywords

Riemannian Manifolds Killing vector fields Rellich identities Pohozaev’s Identity 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Instituto de Matemática, Estatistica e Computação Científica - IMECCUniversidade Estadual de Campinas - UNICAMPCampinasBrasil
  2. 2.Dipartimento di Matematica e InformaticaUniversitá degli Studi di TriesteTriesteItaly

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