Logarithmic convexity of \(L^ 2\) norms for solutions of linear elliptic equations
The author studies the problem \[ {\partial^ 2u \over \partial y^ 2} + \nabla_ x \cdot (A(x,y) \nabla_ xu) = 0 \tag{1} \] in the upper half- space \(\mathbb{R}_ +^{n+1} = \{(x,y) \in \mathbb{R}^ n \times \mathbb{R} \mid y>0\}\) and shows that there exists a function \(h\) such that \(\log \| u(x,h(y)) \|_ 2\) is convex in \(y>0\) for any solution \(u\) of (1).
scientific article; zbMATH DE number 549280