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Some space-time integrability estimates of the solution for heat equations in two dimensions
1. | Mathematical Institute, Tohoku University, Aoba 6-3, Aobaku, Sendai, 980-8578, Japan |
[1] |
Neal Bez, Sanghyuk Lee, Shohei Nakamura, Yoshihiro Sawano. Sharpness of the Brascamp–Lieb inequality in Lorentz spaces. Electronic Research Announcements, 2017, 24: 53-63. doi: 10.3934/era.2017.24.006 |
[2] |
Paolo Maremonti. A remark on the Stokes problem in Lorentz spaces. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1323-1342. doi: 10.3934/dcdss.2013.6.1323 |
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Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119 |
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S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control and Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279 |
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Frédéric Abergel, Jean-Michel Rakotoson. Gradient blow-up in Zygmund spaces for the very weak solution of a linear elliptic equation. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1809-1818. doi: 10.3934/dcds.2013.33.1809 |
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Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153 |
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Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
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Kazuhiro Ishige, Yujiro Tateishi. Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 369-401. doi: 10.3934/dcds.2021121 |
[9] |
Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements, 2014, 21: 109-112. doi: 10.3934/era.2014.21.109 |
[10] |
Naoki Shioji, Kohtaro Watanabe. Uniqueness of positive radial solutions of the Brezis-Nirenberg problem on thin annular domains on $ {\mathbb S}^n $ and symmetry breaking bifurcations. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4727-4770. doi: 10.3934/cpaa.2020210 |
[11] |
Ren-You Zhong, Nan-Jing Huang. Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 261-274. doi: 10.3934/naco.2011.1.261 |
[12] |
Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545 |
[13] |
Anat Amir. Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets. Electronic Research Announcements, 2011, 18: 61-68. doi: 10.3934/era.2011.18.61 |
[14] |
Pierdomenico Pepe. A nonlinear version of Halanay's inequality for the uniform convergence to the origin. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021045 |
[15] |
Mateusz Krukowski. Arzelà-Ascoli's theorem in uniform spaces. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 283-294. doi: 10.3934/dcdsb.2018020 |
[16] |
Bernd Hofmann, Barbara Kaltenbacher, Elena Resmerita. Lavrentiev's regularization method in Hilbert spaces revisited. Inverse Problems and Imaging, 2016, 10 (3) : 741-764. doi: 10.3934/ipi.2016019 |
[17] |
Yong Fang, Patrick Foulon, Boris Hasselblatt. Zygmund strong foliations in higher dimension. Journal of Modern Dynamics, 2010, 4 (3) : 549-569. doi: 10.3934/jmd.2010.4.549 |
[18] |
Isabel Flores. Singular solutions of the Brezis-Nirenberg problem in a ball. Communications on Pure and Applied Analysis, 2009, 8 (2) : 673-682. doi: 10.3934/cpaa.2009.8.673 |
[19] |
Daniele Cassani, Bernhard Ruf, Cristina Tarsi. On the capacity approach to non-attainability of Hardy's inequality in $\mathbb{R}^N$. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 245-250. doi: 10.3934/dcdss.2019017 |
[20] |
Rudolf Ahlswede. The final form of Tao's inequality relating conditional expectation and conditional mutual information. Advances in Mathematics of Communications, 2007, 1 (2) : 239-242. doi: 10.3934/amc.2007.1.239 |
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