Abstract
We will show that if is the solution of log , , in , on , on where is a smooth convex bounded domain, then for the rescaled function log will converge uniformly on every compact subset of to the unique solution of the equation , , in with on as . When , , or , and on , then the function log will converge uniformly on to as where and are the first positive eigenvalue and positive eigenfunction of the Laplace operator on with respectively and .
Citation
Kin Ming Hui. "Asymptotic behaviour of solutions of log u$ in a bounded domain." Differential Integral Equations 14 (2) 175 - 188, 2001. https://doi.org/10.57262/die/1356123351
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