Article citationsMore>>

Bedrossian, J., Gualdani, M. and Snelson, S. (2021) Non-Existence of Some Approximately Self-Similar Singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann Equations. ArXiv: 2105.03942.

has been cited by the following article:

• 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.