General Parabolic Mixed Order Systems in Lp and Applications

種類:

電子ブック

責任表示:

by Robert Denk, Mario Kaip

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2013

著者名:

• Denk, Robert
• Kaip, Mario
• SpringerLink (Online service)

シリーズ名:

Operator Theory: Advances and Applications ; 239

ISBN:

9783319020006 [3319020005]    

注記:

In this text, a theory for general linear parabolic partial differential equations is established, which covers equations with inhomogeneous symbol structure as well as mixed order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity), which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations that are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The latter class appears in a natural way as traces of Lp-Lq-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic pla

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