On the computational complexity of the Dirichlet Problem for Poisson's Equation
Akitoshi Kawamura, Florian Steinberg, Martin Ziegler · Mathematical Structures in Computer Science · 2016
The last years have seen an increasing interest in classifying (existence claims in) classical mathematical theorems according to their strength. We pursue this goal from the refined perspective of computational complexity. Specifically, we establish that rigorously solving the Dirichlet Problem for Poisson's Equation is in a precise sense ‘complete’ for the complexity class ${\#\mathcal{P}}$ and thus as hard or easy as parametric Riemann integration (Friedman 1984; Ko 1991.Complexity Theory of Real Functions).