Elliptic and weakly coercive systems of operators in Sobolev spaces
| dc.creator | Limanskii, D. V. | |
| dc.creator | Malamud, M. M. | |
| dc.date | 2009-04-19 | |
| dc.date.accessioned | 2026-07-07T13:05:53Z | |
| dc.date.available | 2026-07-07T13:05:53Z | |
| dc.description | It is known that an elliptic system $\{P_j(x,D)\}_1^N$ of order $l$ is weakly coercive in $\overset{\circ}{W}\rule{0pt}{2mm}^l_\infty(\mathbb R^n)$, that is, all differential monomials of order $\le l-1$ on $C_0^\infty(\mathbb R^n)$-functions are subordinated to this system in the $L^\infty$-norm. Conditions for the converse result are found and other properties of weakly coercive systems are investigated. An analogue of the de Leeuw-Mirkil theorem is obtained for operators with variable coefficients: it is shown that an operator $P(x,D)$ in $n\ge 3$ variables with constant principal part is weakly coercive in $\overset{\circ}{W}\rule{0pt}{2mm}_\infty^l(\mathbb R^n)$ if and only if it is elliptic. A similar result is obtained for systems $\{P_j(x,D)\}_1^N$ with constant coefficients under the condition $n\ge 2N+1$ and with several restrictions on the symbols $P_j(ξ)$ . A complete description of differential polynomials in two variables which are weakly coercive in $\overset{\circ}{W}\rule{0pt}{2mm}_\infty^l(\mathbb R^2)$ is given. Wide classes of systems with constant coefficients which are weakly coercive in $\overset{\circ}{W}\rule{0pt}{2mm}_\infty^l(\mathbb \R^n)$, but non-elliptic are constructed. | |
| dc.description | 36 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0904.2922 | |
| dc.identifier | http://arxiv.org/abs/0904.2922 | |
| dc.identifier | D.V. Limanskii, M.M. Malamud, Elliptic and weakly coercive systems of operators in Sobolev spaces Sbornik: Mathematics, 199: 11, 1649-1686 (2008) | |
| dc.identifier | doi:10.1070/SM2008v199n11BEH003976 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227634 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J45; 47F05 | |
| dc.title | Elliptic and weakly coercive systems of operators in Sobolev spaces | |
| dc.type | text |