Let u1 and u2 be solution of the equation Delta u=1 in D, u=0 on partial D, where D=(x,y)inR^2/(x-2)^2+(y-1)^2le1/4 and partial D=(x,y)inR^2/(x-2)^2+(y-1)^2=1/4 is the boundary of D. If u1(2,1)=u2(2,1), then:

Q65Section II (Mathematics)65 of 190

Uniqueness for the Dirichlet problem via the maximum principle

Let $u_1$ and $u_2$ be solution of the equation $\Delta u=1$ in D, $u=0$ on $\partial D$ , where $D=\{(x,y)\in\mathbb{R}^2/(x-2)^2+(y-1)^2\le1/4\}$ and $\partial D=\{(x,y)\in\mathbb{R}^2/(x-2)^2+(y-1)^2=1/4\}$ is the boundary of D. If $u_1(2,1)=u_2(2,1)$ , then:

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