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Academic literature on the topic 'Caffarelli-Kohn-Nirenberg equations'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Caffarelli-Kohn-Nirenberg equations"

1

LIN, LISHAN, and ZHAOLI LIU. "MULTI-BUBBLE SOLUTIONS FOR EQUATIONS OF CAFFARELLI–KOHN–NIRENBERG TYPE." Communications in Contemporary Mathematics 13, no. 06 (December 2011): 945–68. http://dx.doi.org/10.1142/s0219199711004518.

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Multi-bubble solutions are constructed for the elliptic equations of Caffarelli–Kohn–Nirenberg type [Formula: see text] where N ≥ 3, [Formula: see text], [Formula: see text], [Formula: see text], a ≤ b < a + 1, K ∈ C(ℝN), K(x) > 0 for x ∈ ℝN, K(x) → 0 as |x| → 0 and |x| → ∞, and ϵ > 0 is a parameter.
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FELLI, VERONICA, and MATTHIAS SCHNEIDER. "COMPACTNESS AND EXISTENCE RESULTS FOR DEGENERATE CRITICAL ELLIPTIC EQUATIONS." Communications in Contemporary Mathematics 07, no. 01 (February 2005): 37–73. http://dx.doi.org/10.1142/s0219199705001623.

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This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli–Kohn–Nirenberg type. By means of blow-up analysis techniques, we prove an a priori estimate in a weighted space of continuous functions. From this compactness result, the existence of a solution to our problem is proved by exploiting the homotopy invariance of the Leray–Schauder degree.
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Abdellaoui, B., and I. Peral. "On quasilinear elliptic equations related to some Caffarelli-Kohn-Nirenberg inequalities." Communications on Pure & Applied Analysis 2, no. 4 (2003): 539–66. http://dx.doi.org/10.3934/cpaa.2003.2.539.

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Dall'Aglio, Andrea, Daniela Giachetti, and Ireneo Peral. "Results on Parabolic Equations Related to Some Caffarelli--Kohn--Nirenberg Inequalities." SIAM Journal on Mathematical Analysis 36, no. 3 (January 2005): 691–716. http://dx.doi.org/10.1137/s0036141003432353.

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Felli, Veronica, and Matthias Schneider. "Perturbation results of critical elliptic equations of Caffarelli–Kohn–Nirenberg type." Journal of Differential Equations 191, no. 1 (June 2003): 121–42. http://dx.doi.org/10.1016/s0022-0396(02)00085-2.

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Musso, Monica, and Juncheng Wei. "Nonradial Solutions to Critical Elliptic Equations of Caffarelli–Kohn–Nirenberg Type." International Mathematics Research Notices 2012, no. 18 (September 14, 2011): 4120–62. http://dx.doi.org/10.1093/imrn/rnr179.

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7

Bouchekif, M., and A. Matallah. "On singular nonhomogeneous elliptic equations involving critical Caffarelli–Kohn–Nirenberg exponent." Ricerche di Matematica 58, no. 2 (August 5, 2009): 207–18. http://dx.doi.org/10.1007/s11587-009-0056-y.

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DENG, YINBIN, LINGYU JIN, and SHUANGJIE PENG. "POSITIVE SOLUTIONS FOR ELLIPTIC EQUATIONS RELATED TO THE CAFFARELLI–KOHN–NIRENBERG INEQUALITIES." Communications in Contemporary Mathematics 11, no. 02 (April 2009): 185–99. http://dx.doi.org/10.1142/s0219199709003338.

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In this paper, we are concerned with the following elliptic problems which are related to the well-known Caffarelli–Kohn–Nirenberg inequalities: [Formula: see text] where a = b < 0, [Formula: see text], a ≤ d ≤ a + 1, a ≤ e ≤ a + 1, [Formula: see text], [Formula: see text], 2 < q < D, λ and η are real constants. We obtain positive solutions for problem (0.1). Moreover, we establish a corresponding Pohozaev identity for problem (0.1), from which, the nonexistence of positive solutions for problem (0.1) is obtained.
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Deng, Zhiying, and Yisheng Huang. "On -symmetric solutions of critical elliptic equations of Caffarelli–Kohn–Nirenberg type." Nonlinear Analysis: Real World Applications 12, no. 2 (April 2011): 1089–102. http://dx.doi.org/10.1016/j.nonrwa.2010.09.002.

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Benmansour, S., and A. Matallah. "Multiple Solutions for Nonhomogeneous Elliptic Equations Involving Critical Caffarelli–Kohn–Nirenberg Exponent." Mediterranean Journal of Mathematics 13, no. 6 (July 8, 2016): 4679–91. http://dx.doi.org/10.1007/s00009-016-0769-6.

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Dissertations / Theses on the topic "Caffarelli-Kohn-Nirenberg equations"

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Felli, Veronica. "Elliptic variational problems with critical exponent." Doctoral thesis, SISSA, 2003. http://hdl.handle.net/20.500.11767/4304.

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van, Heerden Francois A. "Semilinear Elliptic Equations in Unbounded Domains." DigitalCommons@USU, 2004. https://digitalcommons.usu.edu/etd/7146.

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We studied some semilinear elliptic equations on the entire space R^N. Our approach was variational, and the major obstacle was the breakdown in compactness due to the unboundedness of the domain. First, we considered an asymptotically linear Scltrodinger equation under the presence of a steep potential well. Using Lusternik-Schnirelmann theory, we obtained multiple solutions depending on the interplay between the linear, and nonlinear parts. We also exploited the nodal structure of the solutions. For periodic potentials, we constructed infinitely many homoclinic-type multibump solutions. This recovers the analogues result for the superlinear case. Finally, we introduced weights on the linear and nonlinear parts, and studied how their interact ion affects the local and global compactness of the problem. Our approach is based on the Caffarelli-Kohn-Nirenberg inequalities.
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Book chapters on the topic "Caffarelli-Kohn-Nirenberg equations"

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Costa, David G., and Olímpio H. Miyagaki. "On a Class of Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type." In Progress in Nonlinear Differential Equations and Their Applications, 207–20. Basel: Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7401-2_14.

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Chemin, Jean-Yves, Benoit Desjardins, Isabelle Gallagher, and Emmanuel Grenier. "References and Remarks on the Navier–Stokes Equations." In Mathematical Geophysics. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198571339.003.0009.

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The purpose of this chapter is to give some historical landmarks to the reader. The concept of weak solutions certainly has its origin in mechanics; the article by C. Oseen [100] is referred to in the seminal paper by J. Leray. In that famous article, J. Leray proved the global existence of solutions of (NSν) in the sense of Definition 2.5, page 42, in the case when Ω = R3. The case when Ω is a bounded domain was studied by E. Hopf in. The study of the regularity properties of those weak solutions has been the purpose of a number of works. Among them, we recommend to the reader the fundamental paper of L. Caffarelli, R. Kohn and L. Nirenberg. In two space dimensions, J.-L. Lions and G. Prodi proved in [91] the uniqueness of weak solutions (this corresponds to Theorem 3.2, page 56, of this book). Theorem 3.3, page 58, of this book shows that regularity and uniqueness are two closely related issues. In the case of the whole space R3, theorems of that type have been proved by J. Leray in.
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Conference papers on the topic "Caffarelli-Kohn-Nirenberg equations"

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Wolf, Jörg. "A direct proof of the Caffarelli-Kohn-Nirenberg theorem." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-34.

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