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A new proof of the boundedness results for stable solutions to semilinear elliptic equations
We consider the class of stable solutions to semilinear equations $ -\Delta u = f(u) $ in a bounded smooth domain of $ \mathbb{R}^n $. Since 2010 an interior a priori $ L^\infty $ bound for stable solutions is known to hold in dimensions $ n\le 4 $ for all …