We investigate some asymptotic properties of extrema u(alpha) to the two-dimensional variational problem sup integral(B) (e(gamma u2) - 1)vertical bar x vertical bar(alpha)dx e epsilon H1/0(B) vertical bar vertical bar u vertical bar vertical bar= 1 as alpha + infinity. Here B is the unit disk of R-2 and 0 < gamma <= 4 pi is a given parameter. We prove that in a certain range of gamma's, the maximizers are not radial for alpha large.

Symmetry breaking results for problems with exponential growth in the unit disk / S. Secchi, E. Serra. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 8:6(2006), pp. 823-839.

Symmetry breaking results for problems with exponential growth in the unit disk

S. Secchi
Primo
;
E. Serra
Ultimo
2006

Abstract

We investigate some asymptotic properties of extrema u(alpha) to the two-dimensional variational problem sup integral(B) (e(gamma u2) - 1)vertical bar x vertical bar(alpha)dx e epsilon H1/0(B) vertical bar vertical bar u vertical bar vertical bar= 1 as alpha + infinity. Here B is the unit disk of R-2 and 0 < gamma <= 4 pi is a given parameter. We prove that in a certain range of gamma's, the maximizers are not radial for alpha large.
symmetry breaking; Henon-type equations; Trudinger-Moser inequality
Settore MAT/05 - Analisi Matematica
http://www.worldscinet.com/ccm/08/preserved-docs/0806/S0219199706002295.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/24334
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