%0 Journal Article
%T Verification of the Landau Equation and Hardy¡¯s Inequality
%A Salih Yousuf Mohamed Salih
%J Applied Mathematics
%P 208-229
%@ 2152-7393
%D 2023
%I Scientific Research Publishing
%R 10.4236/am.2023.143013
%X We prove the L estimate for the isotropic version of the homogeneous landau problem, which was explored by M. Gualdani and N. Guillen. As shown in a region of the smooth potentials range under values of the interaction exponent (2), a weighted Poincar¨¦ inequality is a natural consequence of the traditional weighted Hardy inequality, which in turn implies that the norms of solutions propagate in the L1 space. Now, the L estimate is based on the work of De Giorgi, Nash, and Moser, as well as a few weighted Sobolev inequalities.
%K Hardy¡¯s Inequality
%K Sobolev Inequalities
%K the Landau Equation
%K L-Estimate
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=123897