Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (v3)

Details Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (v3) Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry (v3)

2010-03-18

arxiv.org/abs/1003.3578v1

Mathematics

Analysis of PDEs

3rd version, (previous versions available separately due to problem with Hal->Arxiv interconnexion)

Scientific paper

We calculate the full asymptotic expansion of boundary blow-up solutions, for
any nonlinearity f. Our approach enables us to state sharp qualitative results
regarding uniqueness and ra-dial 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) = u^p, p > 1.

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