Advances in Differential Equations

Regularity of a very weak solution for parabolic equations and applications

Jean-Michel Rakotoson

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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.

Article information

Source
Adv. Differential Equations Volume 16, Number 9/10 (2011), 867-894.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703179

Mathematical Reviews number (MathSciNet)
MR2850756

Zentralblatt MATH identifier
1231.35033

Subjects
Primary: 35K10: Second-order parabolic equations 35D30: Weak solutions 35K67: Singular parabolic equations 35K65: Degenerate parabolic equations

Citation

Rakotoson, Jean-Michel. Regularity of a very weak solution for parabolic equations and applications. Adv. Differential Equations 16 (2011), no. 9/10, 867--894. https://projecteuclid.org/euclid.ade/1355703179.


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