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Compactness of the gain parts of the linearized Boltzmann operator with weakly cutoff kernels
1. | Department of Mathematics & Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, United States |
2. | Department of Mathematics, University of Maryland, College Park, MD 20742, United States |
[1] |
Andrea Bondesan, Laurent Boudin, Marc Briant, Bérénice Grec. Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium maxwell distributions. Communications on Pure and Applied Analysis, 2020, 19 (5) : 2549-2573. doi: 10.3934/cpaa.2020112 |
[2] |
Pierre Gervais. A spectral study of the linearized Boltzmann operator in $ L^2 $-spaces with polynomial and Gaussian weights. Kinetic and Related Models, 2021, 14 (4) : 725-747. doi: 10.3934/krm.2021022 |
[3] |
Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315 |
[4] |
Ricardo J. Alonso, Irene M. Gamba. Gain of integrability for the Boltzmann collisional operator. Kinetic and Related Models, 2011, 4 (1) : 41-51. doi: 10.3934/krm.2011.4.41 |
[5] |
Joel Coacalle, Andrew Raich. Compactness of the complex Green operator on non-pseudoconvex CR manifolds. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2139-2154. doi: 10.3934/cpaa.2021061 |
[6] |
A. V. Bobylev, E. Mossberg. On some properties of linear and linearized Boltzmann collision operators for hard spheres. Kinetic and Related Models, 2008, 1 (4) : 521-555. doi: 10.3934/krm.2008.1.521 |
[7] |
Miguel Escobedo, Minh-Binh Tran. Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature. Kinetic and Related Models, 2015, 8 (3) : 493-531. doi: 10.3934/krm.2015.8.493 |
[8] |
Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators. Kinetic and Related Models, 2013, 6 (3) : 625-648. doi: 10.3934/krm.2013.6.625 |
[9] |
Shaoqiang Shang, Yunan Cui. Weak approximative compactness of hyperplane and Asplund property in Musielak-Orlicz-Bochner function spaces. Electronic Research Archive, 2020, 28 (1) : 327-346. doi: 10.3934/era.2020019 |
[10] |
Horst R. Thieme. Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 735-764. doi: 10.3934/dcds.1998.4.735 |
[11] |
Melvin Faierman. Fredholm theory for an elliptic differential operator defined on $ \mathbb{R}^n $ and acting on generalized Sobolev spaces. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1463-1483. doi: 10.3934/cpaa.2020074 |
[12] |
Peng Gao. Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2493-2510. doi: 10.3934/dcdsb.2018262 |
[13] |
Yong-Kum Cho. A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem. Kinetic and Related Models, 2012, 5 (3) : 441-458. doi: 10.3934/krm.2012.5.441 |
[14] |
Radjesvarane Alexandre, Lingbing He. Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$. Kinetic and Related Models, 2008, 1 (4) : 491-513. doi: 10.3934/krm.2008.1.491 |
[15] |
Yong-Kum Cho, Hera Yun. On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials. Kinetic and Related Models, 2012, 5 (4) : 769-786. doi: 10.3934/krm.2012.5.769 |
[16] |
Juan Campos, Rafael Obaya, Massimo Tarallo. Recurrent equations with sign and Fredholm alternative. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 959-977. doi: 10.3934/dcdss.2016036 |
[17] |
Marcel Braukhoff. Semiconductor Boltzmann-Dirac-Benney equation with a BGK-type collision operator: Existence of solutions vs. ill-posedness. Kinetic and Related Models, 2019, 12 (2) : 445-482. doi: 10.3934/krm.2019019 |
[18] |
Pavel Jirásek. On Compactness Conditions for the $p$-Laplacian. Communications on Pure and Applied Analysis, 2016, 15 (3) : 715-726. doi: 10.3934/cpaa.2016.15.715 |
[19] |
Carlangelo Liverani. Fredholm determinants, Anosov maps and Ruelle resonances. Discrete and Continuous Dynamical Systems, 2005, 13 (5) : 1203-1215. doi: 10.3934/dcds.2005.13.1203 |
[20] |
Björn Sandstede, Arnd Scheel. Relative Morse indices, Fredholm indices, and group velocities. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 139-158. doi: 10.3934/dcds.2008.20.139 |
2020 Impact Factor: 1.432
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