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2007 Gradient estimates for solutions of parabolic differential equations degenerating at infinity
Alberto Favaron, Alfredo Lorenzi
Adv. Differential Equations 12(4): 435-460 (2007).

Abstract

For $p\in (1,+\infty)$ we derive a weighted $L^p$ estimate for the (spatial) gradient of the solution $u$ of a degenerate parabolic differential equation. Here the underlying domain $\Omega\subset\mathbf{R}^n$, $n\ge 2$, is unbounded and the equation may degenerate only at infinity along some unbounded branch of $\Omega$. Our estimate is strictly related with the still-open problem of giving a concrete characterization of the interpolation space between $W^{2,p}(\Omega)$ and $L^p(\Omega)$ to which the (spatial) gradient of $u$ belongs.

Citation

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Alberto Favaron. Alfredo Lorenzi. "Gradient estimates for solutions of parabolic differential equations degenerating at infinity." Adv. Differential Equations 12 (4) 435 - 460, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1152.35013
MathSciNet: MR2305875

Subjects:
Primary: 35K65
Secondary: 35B45, 35B65

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 4 • 2007
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