Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra. (arXiv:1002.1772v1 [math.AP])

Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra. (arXiv:1002.1772v1 [math.AP]): "

We prove weighted anisotropic analytic estimates for solutions of model
elliptic boundary value problems in polyhedra. The weighted analytic classes
which we use are the same as those introduced by B. Guo in 1993 in view of
establishing exponential convergence for hp methods in polyhedra. We first give
a simple proof of the weighted analytic regularity in a polygon, relying on new
elliptic a priori estimates with analytic control of derivatives in smooth
domains. The technique is based on dyadic partitions near the corners. This
technique can be successfully extended to polyhedra, but only isotropic
analytic regularity can be proved in this way. We therefore combine it with a
nested open set technique to obtain the three-dimensional anisotropic analytic
result. Our proofs are global and do not rely on the analysis of singularities.

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