American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 707-716. doi: 10.3934/proc.2011.2011.707

Some space-time integrability estimates of the solution for heat equations in two dimensions

Norisuke Ioku 1,

1. 

Mathematical Institute, Tohoku University, Aoba 6-3, Aobaku, Sendai, 980-8578, Japan

Received  July 2010 Revised  April 2011 Published  October 2011

We study some space-time integrability estimates for a solution of an inhomogeneous heat equation in $(0,T) \times \Omega$ with 0-Dirichlet boundary condition, where $\Omega$ is a bounded domain in $\mathbb{R}^2$. We also discuss an exponential integrability estimate for the Poisson equation in $\Omega$ with 0-Dirichlet boundary condition.
Keywords: Lorentz-Zygmund spaces, Brezis-Merle's inequality.
Mathematics Subject Classification: Primary:35K05, Secondary:46E30.
Citation: Norisuke Ioku. Some space-time integrability estimates of the solution for heat equations in two dimensions. Conference Publications, 2011, 2011 (Special) : 707-716. doi: 10.3934/proc.2011.2011.707
[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 & Continuous Dynamical Systems - S, 2013, 6 (5) : 1323-1342. doi: 10.3934/dcdss.2013.6.1323
[3]

Frédéric Abergel, Jean-Michel Rakotoson. Gradient blow-up in Zygmund spaces for the very weak solution of a linear elliptic equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1809-1818. doi: 10.3934/dcds.2013.33.1809
[4]

Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119
[5]

S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279
[6]

Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153
[7]

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 & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115
[8]

Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements, 2014, 21: 109-112. doi: 10.3934/era.2014.21.109
[9]

Ren-You Zhong, Nan-Jing Huang. Strict feasibility for generalized mixed variational inequality in reflexive Banach spaces. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 261-274. doi: 10.3934/naco.2011.1.261
[10]

Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545
[11]

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
[12]

Mateusz Krukowski. Arzelà-Ascoli's theorem in uniform spaces. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 283-294. doi: 10.3934/dcdsb.2018020
[13]

Bernd Hofmann, Barbara Kaltenbacher, Elena Resmerita. Lavrentiev's regularization method in Hilbert spaces revisited. Inverse Problems & Imaging, 2016, 10 (3) : 741-764. doi: 10.3934/ipi.2016019
[14]

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
[15]

Isabel Flores. Singular solutions of the Brezis-Nirenberg problem in a ball. Communications on Pure & Applied Analysis, 2009, 8 (2) : 673-682. doi: 10.3934/cpaa.2009.8.673
[16]

Sonja Hohloch, Silvia Sabatini, Daniele Sepe. From compact semi-toric systems to Hamiltonian $S^1$-spaces. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 247-281. doi: 10.3934/dcds.2015.35.247
[17]

Daniele Cassani, Bernhard Ruf, Cristina Tarsi. On the capacity approach to non-attainability of Hardy's inequality in $\mathbb{R}^N$. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 245-250. doi: 10.3934/dcdss.2019017
[18]

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
[19]

Manuel Gutiérrez. Lorentz geometry technique in nonimaging optics. Conference Publications, 2003, 2003 (Special) : 386-392. doi: 10.3934/proc.2003.2003.386
[20]

Sun-Sig Byun, Yunsoo Jang. Calderón-Zygmund estimate for homogenization of parabolic systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6689-6714. doi: 10.3934/dcds.2016091

 Impact Factor: 

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences