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

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

2009-01-27

arxiv.org/abs/0901.4324v2

Mathematics

Analysis of PDEs

Scientific paper

We calculate the full asymptotic expansion of boundary blow-up so- lutions,
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. At
last, we study in more detail the standard nonlinearities f (u) = u^p, p > 1

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