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September/October 2011 Regularity of a very weak solution for parabolic equations and applications
Jean-Michel Rakotoson
Adv. Differential Equations 16(9/10): 867-894 (September/October 2011).

Abstract

In this paper we study the regularity of the so-called very weak solution for a parabolic equation. This unique solution is only integrable over the parabolic cylinder. The initial data and the right-hand side of the linear parabolic equation are functions integrable with respect to the weight function which corresponds to the distance function. In particular, we prove some global regularity of the space-gradient in Lorentz spaces. The regularity with respect to the time derivative is obtained under the condition that the linear operator is time independent and self-adjoint via $m$-accretive theory.

Citation

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Jean-Michel Rakotoson. "Regularity of a very weak solution for parabolic equations and applications." Adv. Differential Equations 16 (9/10) 867 - 894, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1231.35033
MathSciNet: MR2850756

Subjects:
Primary: 35D30, 35K10, 35K65, 35K67

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 9/10 • September/October 2011
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