For any smooth bounded domain (Formula presented.), we consider positive solutions to (Formula presented.)which satisfy the uniform energy bound (Formula presented.)for (Formula presented.). We prove convergence to (Formula presented.) as (Formula presented.) of the (Formula presented.)-norm of any solution. We further deduce quantization of the energy to multiples of (Formula presented.), thus completing the analysis performed in De Marchis et al. (J Fixed Point Theory Appl 19:889–916, 2017).
L∞-norm and energy quantization for the planar Lane–Emden problem with large exponent / de Marchis, F.; Grossi, M.; Ianni, I.; Pacella, F.. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - STAMPA. - (2018), pp. 1-9. [10.1007/s00013-018-1191-z]
L∞-norm and energy quantization for the planar Lane–Emden problem with large exponent
de Marchis, F.Membro del Collaboration Group
;Grossi, M.Membro del Collaboration Group
;Ianni, I.Membro del Collaboration Group
;Pacella, F.Membro del Collaboration Group
2018
Abstract
For any smooth bounded domain (Formula presented.), we consider positive solutions to (Formula presented.)which satisfy the uniform energy bound (Formula presented.)for (Formula presented.). We prove convergence to (Formula presented.) as (Formula presented.) of the (Formula presented.)-norm of any solution. We further deduce quantization of the energy to multiples of (Formula presented.), thus completing the analysis performed in De Marchis et al. (J Fixed Point Theory Appl 19:889–916, 2017).| File | Dimensione | Formato | |
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