Artículos de revistas
Conformal Killing Vector Fields And Rellich Type Identities On Riemannian Manifolds, Ii
Registro en:
Mediterranean Journal Of Mathematics. , v. 9, n. 1, p. 1 - 20, 2012.
16605446
10.1007/s00009-011-0126-8
2-s2.0-84856394905
Autor
Bozhkov Y.
Mitidieri E.
Institución
Resumen
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. © 2011 Springer Basel AG. 9 1 1 20 Bozhkov, Y., Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities (2006) J. Differential Equations, 225, pp. 666-684 Bozhkov, Y., A Caffarelli-Kohn-Nirenberg type inequality on Riemannian manifolds (2010) Applied Mathematics Letters, 23, pp. 1166-1169 Bozhkov, Y., Freire, I.L., Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson Equation (2010) J. Differential Equations, 249, pp. 872-913 Bozhkov, Y., Mitidieri, E., The Noether approach to Pohozaev's Identities (2007) Mediterr. J. Math., 4, pp. 383-405 Bozhkov, Y., Mitidieri, E., Lie symmetries and criticality of semilinear differential systems (2007) SIGMA Symmetry, Integrability and Geometry: Methods and Applications, 3, p. 17. , Paper 053, (electronic) Bozhkov, Y., Mitidieri, E., Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds (2008) I. Lecture Notes of Seminario Interdisciplinare Di Matematica, 7, pp. 65-80 Clément, P., de Figueiredo, D., Mitidieri, E., Positive solutions of semilinear elliptic systems (1992) Comm. in Partial Differential Equations, 17 (5-6), pp. 923-940 Ibragimov, N.H., Noether's identity (1979) Dinamika Sploshn. Sredy No., 38, pp. 26-32. , (Russian) Ibragimov, N.H., Transformation groups applied to mathematical physics (1985) Translated from the Russian Mathematics and its Applications, , (Soviet Series), D. Reidel Publishing Co., Dordrecht Mitidieri, E., (1990) A Rellich identity and applications, p. 35. , Rapporti interni n. 25, Univ. Udine Mitidieri, E., A Rellich type identity and applications (1993) Commun. in Partial Differential Equations, 18 (1-2), pp. 125-151 Mitidieri, E., Nonexistence of positive solutions of semilinear elliptic systems in ℝ N (1996) Differential Integral Equations, 9, pp. 465-479 Mitidieri, E., A simple approach to Hardy inequalities (2000) Mat. Zametki, 67, pp. 563-572. , (In English: Math. Notes 67 (2000), 479 - 486.) Noether, E., Invariante Variationsprobleme. Nachrichten von der Kön. Ges. der Wissenschaften zu Göttingen (1918) Math.-Phys. Kl, (2), pp. 235-257. , (English translation in: Transport Theory and Statistical Physics 1(3), (1971), 186-207.) Olver, P., (1986) Applications of Lie Groups to Differential Equations, , New York: Springer Pohozaev, S.I., On the eigenfunctions of the equation Δu + λf(u) = 0 (1965) Dokl. Akad. Nauk SSSR, 165, pp. 36-39. , (In English: Soviet Math. Dokl. 6 (1965), 1408 - 1411.) Pohozaev, S.I., On eigenfunctions of quasilinear elliptic problems (1970) Mat. Sb, 82, pp. 192-212. , (In English: Math. USSR Sbornik 11 (1970), 171 - 188.) Pucci, P., Serrin, J., A general variational identity (1986) Indiana Univ. Math. J, 35 (3), pp. 681-703 Rellich, F., Halbbeschränkte Differentialoperatoren höherer Ordnung (1954) Proceedings of the International Congress of Mathematicians, III, pp. 243-250. , Amsterdam, Erven P. Noordhoff N. V., Groningen North-Holland Publishing Co., 1956 Yano, K., (1957) The theory of Lie derivatives and its applications, , North-Holland Publishing Co