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

Norisuke Ioku

doi:10.3934/proc.2011.2011.707

Article Contents

2011, Volume 2011: 707-716. Doi: 10.3934/proc.2011.2011.707 open access

This issue Previous Article On critical exponent for an elliptic equation with non-Lipschitz nonlinearity Next Article Motion of polygonal curved fronts by crystalline motion: v-shaped solutions and eventual monotonicity

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

Received: July 2010

Revised: April 2011

Published: August 2017

Abstract Related Papers Cited by

Abstract

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:

Article Metrics

HTML views() PDF downloads(77) Cited by(0)

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

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

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

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content