L∞-norm and energy quantization for the planar Lane–Emden problem with large exponent

2018

ARCHIV DER MATHEMATIK

L∞-norm and energy quantization for the planar Lane–Emden problem with large exponent

01 Pubblicazione su rivista

de Marchis F., Grossi M., Ianni I., Pacella F.

ISSN: 0003-889X

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).

asymptotic analysis Green’s function Lane–Emden problem Mathematics (all) positive solutions Quantization