Criteria for the $L^{p}$-dissipativity of systems of second order differential equations
| dc.creator | Cialdea, Alberto | |
| dc.creator | Maz'ya, Vladimir | |
| dc.date | 2006-02-17 | |
| dc.date.accessioned | 2026-07-07T07:03:33Z | |
| dc.date.available | 2026-07-07T07:03:33Z | |
| dc.description | We give complete algebraic characterizations of the $L^{p}$-dissipativity of the Dirichlet problem for some systems of partial differential operators of the form $\partial_{h}({\mathscr A}^{hk}(x)\partial_{k})$, were ${\mathscr A}^{hk}(x)$ are $m\times m$ matrices. First, we determine the sharp angle of dissipativity for a general scalar operator with complex coefficients. Next we prove that the two-dimensional elasticity operator is $L^{p}$-dissipative if and only if $$ ({1\over 2}-{1\over p})^{2} \leq {2(ν-1)(2ν-1)\over (3-4ν)^{2}}, $$ $ν$ being the Poisson ratio. Finally we find a necessary and sufficient algebraic condition for the $L^{p}$-dissipativity of the operator $\partial_{h} ({\mathscr A}^{h}(x)\partial_{h})$, where ${\mathscr A}^{h}(x)$ are $m\times m$ matrices with complex $L^{1}_{\rm loc}$ entries, and we describe the maximum angle of $L^{p}$-dissipativity for this operator. | |
| dc.description | 42 pages, LaTeX, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0602382 | |
| dc.identifier | http://arxiv.org/abs/math/0602382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109011 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 47D03 (Primary) 47D06, 47B44, (Secondary)74B05 | |
| dc.title | Criteria for the $L^{p}$-dissipativity of systems of second order differential equations | |
| dc.type | text |