Parameter-Elliptic Fourier Multipliers Systems and Generation of Analytic and C∞ Semigroups

被引：0

作者：

Martinez, Bienvenido Barraza ^{[1
]}

Ospino, Jonathan Gonzalez ^{[1
]}

Acuna, Rogelio Grau ^{[1
]}

Monzon, Jairo Hernandez ^{[1
]}

机构：

[1] Univ Norte, Dept Matemat & Estadist, Barranquilla, Colombia

来源：

MATHEMATICS | 2022年 / 10卷 / 05期

关键词：

C-infinity-semigroups; analytic semigroups; Fourier multipliers; -ellipticity; PSEUDODIFFERENTIAL-OPERATORS; REGULARITY;

D O I：

10.3390/math10050751

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Fourier multiplier systems on R-n with components belonging to the standard Hormander class S-1,0(m) (R-n), but with limited regularity. Using a notion of parameter-ellipticity with respect to a subsector lambda & SUB;C (introduced by Denk, Saal, and Seiler) we show the generation of both C-& INFIN; semigroups and analytic semigroups (in a particular case) on the Sobolev spaces W-p(k & nbsp;)(R-n,C-q) with k & ISIN;N-0, 1 & LE;p <& INFIN; and q & ISIN;N. For the proofs, we modify and improve a crucial estimate from Denk, Saal and Seiler, on the inverse matrix of the symbol (see Lemma 2). As examples, we apply the theory to solve the heat equation, a linear thermoelastic plate equation, a structurally damped plate equation, and a generalized plate equation, all in the whole space, in the frame of Sobolev spaces.

引用

页数：19