Author(s)

Salih Yousuf Mohamed Salih

Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym, Sudan.

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.

Hardy’s Inequality, Sobolev Inequalities, the Landau Equation, L-Estimate

Salih, S. (2023) Verification of the Landau Equation and Hardy’s Inequality. Applied Mathematics, 14, 208-229. doi: 10.4236/am.2023.143013.