The main goal of this project is to study partial regularity of stationary and stable solutions to the Gelfand-Liouville equation. Due to the presence of the exponential nonlinearity, the natural scale invariant energy is not monotone increasing. To overcome this difficulty we propose to study these problems by analyzing the behavior of solutions around singular points, and a blow-up arguments. This involves compactness properties for a family of solutions and understanding homogeneous solutions on the whole Euclidean space.
Tifr - Centre For Applicable Mathematics
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