Pathological solutions to elliptic problems in divergence form with continuous coefficients

Tianling Jin, Vladimir Maz'ya, Jean Van Schaftingen

We construct a function $u\in W_{\mathrm{loc}}^{1,1}(B(0,1))$ which is a solution to $\Div (A \nabla u)=0$ in the sense of distributions, where $A$ is continuous and $u \not \in…