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Tagged with schrodinger-operators regularity
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Nonlinear quadratic Schrödinger equation with variable coefficients
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) = ...
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A question about the regularity of the Schrödinger equation
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 \\
\...