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Verification of the Landau Equation and Hardy’s Inequality
Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym, Sudan
- 1 Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym, Sudan
Applied Mathematics·Volume 14 (2023)·Pages 208–229·Published 13 March 2023·DOI10.4236/am.2023.143013
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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.
KeywordsHardy’s InequalitySobolev Inequalitiesthe Landau EquationL-Estimate
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