Single-point Condensation and Least-energy Solutions
نویسندگان
چکیده
We prove a conjecture raised in our earlier paper which says that the least-energy solutions to a two dimensional semilinear problem exhibit single-point condensation phenomena as the nonlinear exponent gets large. Our method is based on a sharp form of a well-known borderline case of the Sobolev embedding theory. With the help of this embedding, we can use Moser iteration scheme to carefully estimate the upper bound of the solutions. We can also determine the location of the condensation points.
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تاریخ انتشار 2010