Boundary blow-up solutions in the unit ball: Asymptotics, uniqueness and symmetry |
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| Authors: | O Costin |
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| Institution: | a Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174, USA
b LAMFA, UMR CNRS 6140, Université Picardie Jules Verne, 33, rue St Leu, 80039 Amiens, France |
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| Abstract: | We calculate the full asymptotic expansion of boundary blow-up solutions (see Eq. (1) below), for any nonlinearity f. Our approach enables us to state sharp qualitative results regarding uniqueness and radial symmetry of solutions, as well as a characterization of nonlinearities for which the blow-up rate is universal. Lastly, we study in more detail the standard nonlinearities f(u)=up, p>1. |
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