Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

DeepDyve requires Javascript to function. Please enable Javascript on your browser to continue.

General Parabolic Mixed Order Systems in Lp and Applications

Part of the Operator Theory: Advances and Applications Book Series (volume 239)

DOI: 10.1007/978-3-319-02000-6

ISBN: 978-3-319-01999-4

Publisher: Springer International Publishing - Springer Journals

Oct 25, 2013

LitStream

Chapter 1Introduction and Outline

Denk, Robert; Kaip, Mario

Pages: 1 –10

[For more than 50 years, elliptic and parabolic partial di_erential equations have been treated by an investigation of their symbols. This approach is based on the simple observation that the Fourier transform changes spatial derivatives into multiplication with covariables that can be handled...
LitStream

Chapter 2The joint time-space H∞-calculus

Denk, Robert; Kaip, Mario

Pages: 11 –67

[One of the most successful approaches in the theory of partial di_erential equations is based on the Fourier transform and the symbols of di_erential operators and their inverses. The Fourier transform maps di_erentiation into multiplication by the covariable and thus directly leads to a...
LitStream

Chapter 3The Newton polygon approach for mixed-order systems

Denk, Robert; Kaip, Mario

Pages: 69 –141

[Solvability results in elliptic and parabolic theory are in many cases based on estimates of the symbols of the related operators. In classical elliptic and parabolic theory, these symbols are (quasi-)homogeneous. In this case, the condition that the symbol does not vanish automatically implies...
LitStream

Chapter 4Triebel-Lizorkin spaces and the Lp-Lq-setting

Denk, Robert; Kaip, Mario

Pages: 143 –185

[In this chapter we want to generalize the results of Section 2.3 on mixed-order systems to the scale of Triebel-Lizorkin spaces. Triebel-Lizorkin spaces naturally appear in parabolic Lp-Lq-theory as the trace spaces of the solution.]
LitStream

Chapter 5Application to parabolic differential equations

Denk, Robert; Kaip, Mario

Pages: 187 –228

[In this chapter we present a selection of applications of our main result on mixedorder systems stated in Theorem 2.69, Theorem 3.41, Corollary 2.80, and Corollary 3.44. The applications split into two subgroups of parabolic partial differential equations. In the first part we consider problems...

results per page

Prev
1
Next

Browse All eBooks