On the maximal \(L _{p }\)-regularity of parabolic mixed-order systems. (English) Zbl 1242.35221
The paper aims to a general study of parabolic boundary value problems. With respect to preceding contributions [the first author and L. R. Volevich, J. Evol. Equ. 8, No. 3, 523–556 (2008; Zbl 1166.35335)], here the analysis is extended from partial differential operators with constant coefficients to general pseudodifferential operators, in the setting of \(L^p\)-Sobolev spaces of Bessel potential or Besov type. An important technical tool is given by the concept of Volterra pseudodifferential operator, see e.g. [A. Piriou, Ann. Inst. Fourier 20, No. 1, 77–94 (1970; Zbl 0186.20403)]. As applications, the authors discuss time-dependent Douglis-Nirenberg systems and a linear system arising in the study of the Stefan problem with Gibbs-Thomson correction.
Reviewer: Luigi Rodino (Torino)
MSC:
| 35S11 | Initial-boundary value problems for pseudodifferential operators (MSC2010) |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35G40 | Initial value problems for systems of linear higher-order PDEs |
| 35R35 | Free boundary problems for PDEs |
Keywords:
pseudodifferential operators; mixed-order systems; maximal regularity; Volterra pseudodifferential operator; Gibbs-Thomson correctionReferences:
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