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Consider the following quadratic Schrödinger equation in $Q_T = \Omega \times [0,T]$: $$\begin{cases} i \partial_t u + \kappa(x,t) \Delta u + \beta(x,t) u^2 = f(x,t)\\ u(x,0) = ...

While reading the article [1], I noticed I don't understand part of the proof of regularity. For the Schrödinger eigenvalue problem, \begin{cases} -\Delta u+Vu=\lambda u, &\text{in } \Omega \\ \...