# Local solvability of some classes of linear differential operators with multiple characteristics

Local solvability of some classes of linear differential operators with multiple characteristics Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 263-274 (1999) Local Solvability of some Classes of Linear Differential Operators with Multiple Characteristics. P. R. POPIVANOV(*) To the memory of Lamberto Cattabriga In this paper we consider a class of linear partial differential operators (PDO) having smooth coefficients and characteristics of constant multiplicity. The results here obtained can be viewed as a generalization of some theorems in our paper [4]. Thus, let m be an odd integer m I> 3 and the symbol P(x, ~) of the differential operator P(x, D) can be written in the form (1) P(x, ~) = (p(x, ~))m + p~_l(x, ~) +... + po(x, ~), where ord, p~-5 = m -j, p is a first order real valued symbol of principal type, i.e. p(Q0) = 0, ~0 = (x o, ~o) ~ T*(Y2)\O ~ d~p(Q ~ # O. We introduce now several well-known notions, namely: :8 = char p = {(x, ~) e T*(~2)\: p(x, ~) = 0}. Obviously, X is a smooth manifold, codim X = 1. The subprincipal symbol p~ _ 1 of the operator P is given by the formula a2pm (x, ~) (2) p~n-l(X, ~) =Pm-l(X, ~) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

# Local solvability of some classes of linear differential operators with multiple characteristics

, Volume 45 (1) – Jan 1, 1999
12 pages

/lp/springer-journals/local-solvability-of-some-classes-of-linear-differential-operators-e7gzYrfsGa

# References (10)

Publisher
Springer Journals
Copyright © Università degli Studi di Ferrara 1999
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/bf02826099
Publisher site
See Article on Publisher Site

### Abstract

Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 263-274 (1999) Local Solvability of some Classes of Linear Differential Operators with Multiple Characteristics. P. R. POPIVANOV(*) To the memory of Lamberto Cattabriga In this paper we consider a class of linear partial differential operators (PDO) having smooth coefficients and characteristics of constant multiplicity. The results here obtained can be viewed as a generalization of some theorems in our paper [4]. Thus, let m be an odd integer m I> 3 and the symbol P(x, ~) of the differential operator P(x, D) can be written in the form (1) P(x, ~) = (p(x, ~))m + p~_l(x, ~) +... + po(x, ~), where ord, p~-5 = m -j, p is a first order real valued symbol of principal type, i.e. p(Q0) = 0, ~0 = (x o, ~o) ~ T*(Y2)\O ~ d~p(Q ~ # O. We introduce now several well-known notions, namely: :8 = char p = {(x, ~) e T*(~2)\: p(x, ~) = 0}. Obviously, X is a smooth manifold, codim X = 1. The subprincipal symbol p~ _ 1 of the operator P is given by the formula a2pm (x, ~) (2) p~n-l(X, ~) =Pm-l(X, ~)

### Journal

ANNALI DELL UNIVERSITA DI FERRARASpringer Journals

Published: Jan 1, 1999

Keywords: Multiple Characteristic; Cauchy Data; Linear Differential Operator; Local Solvability; Linear Partial Differential Operator

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