Criteria for the $L^{p}$-dissipativity of systems of second order differential equations

Details Criteria for the $L^{p}$-dissipativity of systems of second order differential equations Criteria for the $L^{p}$-dissipativity of systems of second order differential equations

2006-02-17

arxiv.org/abs/math/0602382v1

Mathematics

Analysis of PDEs

42 pages, LaTeX, no figures

Scientific paper

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 $$ ({1\over 2}-{1\over p})^{2} \leq {2(\nu-1)(2\nu-1)\over (3-4\nu)^{2}}, $$ $\nu$ 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.

Affiliated with

Also associated with

No associations

Rating

Criteria for the $L^{p}$-dissipativity of systems of second order differential equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Criteria for the $L^{p}$-dissipativity of systems of second order differential equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Criteria for the $L^{p}$-dissipativity of systems of second order differential equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471362