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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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One question about Theorem 4 in Brezis–Merle's famous paper

I'm reading Theorem 4 of the paper "Uniform Estimates and Blow-up Analysis for Solutions of $-\Delta u = V(x) e^u$ in Two Dimensions" by Brezis and Merle, and at the beginning of the proof they say t …
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