Let g be a locally Lipschitz continuous function defined on R. We assume that g satisfies the Keller-Osserman condition and there exists a positive real number a such that g is convex on [a, infinity). Then any solution it of -Delta u + g(u) = 0 in a ball B of R-N, N >=, 2, which tends to infinity on aB, is spherically symmetric.
Porretta, A., Veron, L. (2006). Symmetry of large solutions of semilinear elliptic equations. COMPTES RENDUS MATHÉMATIQUE, 342(7), 483-487 [10.1016/j.crma.2006.01.020].
Symmetry of large solutions of semilinear elliptic equations.
PORRETTA, ALESSIO;
2006-01-01
Abstract
Let g be a locally Lipschitz continuous function defined on R. We assume that g satisfies the Keller-Osserman condition and there exists a positive real number a such that g is convex on [a, infinity). Then any solution it of -Delta u + g(u) = 0 in a ball B of R-N, N >=, 2, which tends to infinity on aB, is spherically symmetric.File in questo prodotto:
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