Share on Pinterest Exercise gives the brain a boost, and may help protect against cognitive decline, but why? Image credit: NICK VEASEY/SCIENCE PHOTO LIBRARY/Getty Images. Exercise can stimulate brain ...

Consider solving the Dirichlet problem $$\Delta u(P) = 0, P \in \mathbb R^2\backslash S,$$ $$u(P) = h(P),\quad P \in S,$$ $$\sup|u(P)| < \infty,$$ $$P \in \Bbb{R}^2 ...