A compactly supported solution to a three-dimensional uniformly elliptic equation without zero-order term (Q596596)

The author constructs for any \(1< p< 3\) a second-order, nonvariational, elliptic operator \(L\) and a function \(V\) in \(\mathbb{R}^3\) with the following properties: the operator \(L\) is uniformly elliptic, without zero-order term and smooth almost everywhere in \(\mathbb{R}^3\), the function \(V\) is in \(W^{2,p}(\mathbb{R}^3)\), solves the equation \(LV= 0\) in \(\mathbb{R}^3\), it has compact support but it is not identically zero.