1,721,027 research outputs found
A priori estimates, positivity results, and nonexistence of theorems for quasilinear degenerate elliptic inequalities
No full textA priori bounds for solutions of a wide class of quasilinear degenerate elliptic inequalities are proved.
As an outcome we deduce sharp Liouville theorems. Our investigation includes inequalities associated to
p-Laplacian and the mean curvature operators in Carnot groups setting. No hypotheses on the solutions
at infinity are assumed. General results on the sign of solutions for quasilinear coercive/noncoercive inequalities are considered. Related applications to population biology and chemical reaction theory are also studied
Entire solutions of quasilinear elliptic systems on Carnot Groups
No full textWe prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results are new even in the Euclidean setting
Conformal Killing Vector Fields And Rellich Type Identities On Riemannian Manifolds, Ii
No full textWe 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.91120Bozhkov, Y., Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities (2006) J. Differential Equations, 225, pp. 666-684Bozhkov, Y., A Caffarelli-Kohn-Nirenberg type inequality on Riemannian manifolds (2010) Applied Mathematics Letters, 23, pp. 1166-1169Bozhkov, 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. 872-913Bozhkov, Y., Mitidieri, E., The Noether approach to Pohozaev's Identities (2007) Mediterr. J. Math., 4, pp. 383-405Bozhkov, 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. 65-80Clément, P., de Figueiredo, D., Mitidieri, E., Positive solutions of semilinear elliptic systems (1992) Comm. in Partial Differential Equations, 17 (5-6), pp. 923-940Ibragimov, 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., DordrechtMitidieri, E., (1990) A Rellich identity and applications, p. 35. , Rapporti interni n. 25, Univ. UdineMitidieri, E., A Rellich type identity and applications (1993) Commun. in Partial Differential Equations, 18 (1-2), pp. 125-151Mitidieri, E., Nonexistence of positive solutions of semilinear elliptic systems in ℝ N (1996) Differential Integral Equations, 9, pp. 465-479Mitidieri, 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: SpringerPohozaev, 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. 681-703Rellich, F., Halbbeschränkte Differentialoperatoren höherer Ordnung (1954) Proceedings of the International Congress of Mathematicians, III, pp. 243-250. , Amsterdam, Erven P. Noordhoff N. V., GroningenNorth-Holland Publishing Co., 1956Yano, K., (1957) The theory of Lie derivatives and its applications, , North-Holland Publishing C
Nonnegative solutions of some quasilinear elliptic inequalities and applications
No full textAbstract. Let f : R ! R be a continuous function. It is shown that
under certain assumptions on f and A: R ! R+ weak C 1 solutions of the differential inequality −div(A(|ru|)ru) > f(u) on RN are nonnegative.
Some extensions of the result in the framework of subelliptic operators on Carnot groups are considered
A priori estimates and reduction principles for quasilinear elliptic problems and applications
No full textA priori estimate of of solutions of quasilinear elliptic equations are a subject of vital
interest in recent years. Most of the results are dealing with nonnegative solutions and
nonlinearities with denite sign. Recently, Serrin [25] considered Liouville theorems for
quasilinear equations with source term changing sign. These results are consequence of
appropriate a priori estimates on the possible solutions
An application of Kato’s inequality to quasilinear elliptic problems
No full textLet L be a general second order differential elliptic operator.
By using a quasilinear version of Kato’s inequality, we prove that the
only weak solution of the problem
L(u) = |u|^(q−1) u
on
RN ,
q > p − 1,
is u = 0. Here p ≥ 1 is related to L
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