Advances in Differential Equations

Sobolev-Morrey spaces associated with evolution equations

Jens A. Griepentrog

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In this text we introduce new classes of Sobolev--Morrey spaces being adequate for the regularity theory of second-order parabolic boundary-value problems on Lipschitz domains of space dimension $n \ge 3$ with nonsmooth coefficients and mixed boundary conditions. We prove embedding and trace theorems as well as invariance properties of these spaces with respect to localization, Lipschitz transformation, and reflection. In the second part [11] of our presentation we show that the class of second-order parabolic systems with diagonal principal part generates isomorphisms between the above-mentioned Sobolev--Morrey spaces of solutions and right-hand sides.

Article information

Adv. Differential Equations Volume 12, Number 7 (2007), 781-840.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 35K57: Reaction-diffusion equations 35R20: Partial operator-differential equations (i.e., PDE on finite- dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx] 47N20: Applications to differential and integral equations


Griepentrog, Jens A. Sobolev-Morrey spaces associated with evolution equations. Adv. Differential Equations 12 (2007), no. 7, 781--840.

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