An Lp-approach for the study of degenerate parabolic equations

Date

2005-03-29

Authors

Labbas, Rabah
Medeghri, Ahmed
Sadallah, Boubaker-Khaled

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Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

We give regularity results for solutions of a parabolic equation in non-rectangular domains U = ∪t∈]0, 1[</sub> {t} x It with It = {x : 0 < x < φ(t)}. The optimal regularity is obtained in the framework of the space Lp with p > 3/2 by considering the following cases: (1) When φ(t) = tα, α > 1/2 with a p > 1 + α. We use Labbas-Terreni results [11]. (2) When φ(t) = t1/2 with a right-hand side taken only in Lp(U). Our approach make use of the celebrated Dore-Venni results [2].

Description

Keywords

Sum of linear operators, Diffusion equation, Non rectangular domain, Bounded imaginary powers of operators

Citation

Labbas, R., Medeghri, A., & Sadallah, B. K. (2005). An Lp-approach for the study of degenerate parabolic equations. <i>Electronic Journal of Differential Equations, 2005</i>(36), pp. 1-20.

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Attribution 4.0 International

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