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We establish the classification of minimal mass blow-up solutions of the$L^2$ critical inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_t u+ \Delta u + |x|^{-b}|u|^{\frac{4-2b}{N}}u = 0, \] thereby extending thecelebrated result of Merle from the classic case $b=0$ to the case$0<b<\min\{2,N\}$, in any dimension $N\ge1$.

Classification of minimal mass blow-up solutions for an $L^2$ critical inhomogeneous NLS