12-12
Uniform estimates for polyharmonic Green functions in domains with small holes
Hans-Christoph Grunau, Frederic Robert
Preprint series: 12-12 , Preprints
- MSC:
- 35J40 Boundary value problems for higher-order, elliptic equations
- 35B50 Maximum principles
Abstract: We show that in domains in R^n with arbitrarily small smooth holes, the k-polyharmonic Green function (n>2k) can be estimated by C |x-y|^{2k-n}, i.e. a multiple of the polyharmonic singular solution. The key point is that the constant can be chosen independently of the size of the holes. According to more classical results one would have
expected this constant to blow up as the holes shrink to a point.
Keywords: polyharmonic Green function, small holes, uniform estimates
Upload: 2012-10-22-10-22