Global pointwise estimates for Green's matrix of second order elliptic systems

Details Global pointwise estimates for Green's matrix of second order elliptic systems Global pointwise estimates for Green's matrix of second order elliptic systems

2010-01-15

arxiv.org/abs/1001.2618v2

J. Differential Equations 249 (2010) 2643--2662

Mathematics

Analysis of PDEs

17 pages, accepted in J. Differential Equations, references added

Scientific paper

10.1016/j.jde.2010.05.017

We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate. Moreover, we prove that such a local boundedness estimate for weak solutions of the system is equivalent to the usual global pointwise bound for the Green's matrix. In the scalar case, such an estimate is a consequence of De Giorgi-Moser-Nash theory and holds for equations with bounded measurable coefficients in arbitrary domains. In the vectorial case, one need to impose certain assumptions on the coefficients of the system as well as on domains to obtain such an estimate. We present a unified approach valid for both the scalar and vectorial cases and discuss several applications of our result.

Affiliated with

Also associated with

No associations

Rating

Global pointwise estimates for Green's matrix of second order elliptic systems 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 Global pointwise estimates for Green's matrix of second order elliptic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global pointwise estimates for Green's matrix of second order elliptic systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356318