The Problem is the following, I want to use NDSolveValue to solve for specific Dirichlet Conditions, therefore I need to construct a region with ImplicitRegion which has those boundaries I need for my Dirichlet conditions. While it works very good in two dimensions, I fail in three dimensions, because the interior boundaries are not good. For example, let's construct a hollow cylinder with some width:
\[ScriptCapitalR] =
ImplicitRegion[
10 >= x^2 + y^2 >= 1 && 0 <= z <= 10, {x, y,
z}]; RegionPlot3D[\[ScriptCapitalR]]
Looking on the graph, one can see that the interior has not the form of a cylinder, thus defining a Dirichlet condition with x^2 + y^2 == 1 will lead to an error (effectively being ignored) while x^2+y^2 ==10 will be processed. Interestingly, the same problem arises if one wants to construct a hollow cylinder. Has anyone a solution for my problem?