Let \(\Omega\) be a bound domain in Rn with smooth boundary. Consider the following elliptic boundary valued problem: \[ \begin{split}

   \Delta u &= f \quad \text{in \(\Omega\)}\\
    Xu &= g\quad \text{on the boundary}

\end{split} \] Here \(X\) is a transversal vector field to the boundary. This includes the regular Dirichlet and Neumann problem. In this talk, we first introduce suitable Hardy spaces \(H_p(\Omega)\) on \(\Omega\). Then we shall show the inequality \[

\text{norm of second partial differential of $f$} \leq \text{const * norm of $f$}

\]

• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 

21 images

[<6>]