grandes-ecoles 2015 QIV.C.2

grandes-ecoles · France · centrale-maths2__psi Proof Computation of a Limit, Value, or Explicit Formula
We work on $\mathbb{R}^n$ for a natural integer $n \geqslant 3$. We admit that the Dirichlet problem on the unit ball of $\mathbb{R}^n$, associated with a continuous function defined on the unit sphere $S_n(0,1)$, admits a unique solution. Let $m \in \mathbb{N}^*$.
Determine the dimension of $\mathcal{H}_m$ as a function of $m$ and $n$. 
We work on $\mathbb{R}^n$ for a natural integer $n \geqslant 3$. We admit that the Dirichlet problem on the unit ball of $\mathbb{R}^n$, associated with a continuous function defined on the unit sphere $S_n(0,1)$, admits a unique solution. Let $m \in \mathbb{N}^*$.

Determine the dimension of $\mathcal{H}_m$ as a function of $m$ and $n$.
Paper Questions
QI.A.1 QI.A.2 QI.B.1 QI.B.2 QI.B.3 QI.C.1 QI.C.2 QII.A QII.B.1 QII.B.2 QII.B.3 QII.C.1 QII.C.2 QII.D.1 QII.D.2 QII.D.3 QII.D.4 QIII.A.1 QIII.A.2 QIII.A.3 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2