Abstract:
A new proof based on F. Browder's ideology is given for the theorem on the approximation of weak solutions of the Laplace equation in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, with a connected Lipschitz boundary by harmonic polynomials in the Lebesgue space $L_p(\Omega)$ and the Sobolev space $W_p^1(\Omega)$.
Key words:approximation problem, harmonic polynomials, bounded domain in $\mathbb{R}^n$, Lipschitz boundary, Lebesgue space $L_p(\Omega)$, Sobolev space $W_p^1(\Omega)$, weak solutions of the Laplace equation.
References