TITLE:
Verification of the Landau Equation and Hardy’s Inequality
AUTHORS:
Salih Yousuf Mohamed Salih
KEYWORDS:
Hardy’s Inequality, Sobolev Inequalities, the Landau Equation, L-Estimate
JOURNAL NAME:
Applied Mathematics,
Vol.14 No.3,
March
28,
2023
ABSTRACT: 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 Poincaré 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.