In the Caffarelli-Silvestre paper link of paper before Lemma 4.2, it is given that \begin{align} \text{div}(|y|^a \nabla u)=0 ~~~\text{in the weak sense in} ~B_R\\ u=g \hspace{3.3cm}\text{on}~\partial B_R \end{align} has a unique solution in the weighted Sobolev Space $H^{1,2}(B_R,|y|^a)$. I am not getting the exact reference where the existence of solution (unique) is given. Can anybody help me out?
2026-03-28 05:23:20.1774675400
Caffarelli-Silvestre Extension problem (Existence of Solution of Degenerate elliptic PDEs in a ball)
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