Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions

Details Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions

2007-05-23

arxiv.org/abs/0705.3301v4

Mathematics

Analysis of PDEs

Updated version. To appear in "Archive for Rational Mechanics and Analysis"

Scientific paper

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or -- equivalently -- a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem {from} being reasonably written as a system of second order boundary value problems. It is shown that, on the other hand, for bounded smooth domains $\Omega \subset\mathbb{R}^n$, the negative part of the corresponding Green's function is "small" when compared with its singular positive part, provided $n\ge 3$. Moreover, the biharmonic Green's function in balls $B\subset\mathbb{R}^n$ under Dirichlet (i.e. clamped) boundary conditions is known explicitly and is positive. It has been known for some time that positivity is preserved under small regular perturbations of the domain, if $n=2$. In the present paper, such a stability result is proved for $n\ge 3$. Keywords: Biharmonic Green's functions, positivity, almost positivity, blow-up procedure.

Affiliated with

Also associated with

No associations

Rating

Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions 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 Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positivity and almost positivity of biharmonic Green's functions under Dirichlet boundary conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-401282