Local solvability of first order linear operators with Lipschitz coefficients
Let \(L=\partial /\partial t+i\sum^{n}_{j=1}b_ j(x,t)\partial /\partial x_ j+c(x,t)\) with \(b_ j(x,t)\) smooth and real. Let \(Lu=f\). This article shows that Lipschitz continuity of \(b_ j(x,t)\) is sufficient to obtain \(L^ 2\)- solvability and the solution of \(Lu=f\) can be defined on the whole strip \(| t| <\epsilon\).
scientific article; zbMATH DE number 4208632