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math.AP2026
Estimates of the Poincare constants for bounded domains in Euclidian space R^n
Bernd Rummler, Gudrun Thäter
We study bounded, simply connected, convex, and C2-smooth domains in the space R^n for finite n greater than 1. For such domains we use the diameter to find balls with the property…
math.AP2026
Explicit formulas for gradients and the divergence in n-dimensional spherical coordinates
Bernd Rummler, Gudrun Thäter
We use the Laplacian in n-dimensional spherical coordinates (n>1) to write the divergence of a vector field defined on radially symmetric domains in the context of vector calculus.…
math.AP2026
Exact Poincare Constants in n-dimensional Annuli
Bernd Rummler, Michael Ruzicka, Gudrun Thäter
We study -dimensional annuli for with . We choose a non-dimensional setting such that for any fixed and given number the…