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 interactio...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.展开更多
In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new esti...In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.展开更多
The Schwarz method for a class of elliptic variational inequalities with noncoercive operator was studied in this work. The author proved the error estimate in L∞-norm for two domains with overlapping nonmatching gri...The Schwarz method for a class of elliptic variational inequalities with noncoercive operator was studied in this work. The author proved the error estimate in L∞-norm for two domains with overlapping nonmatching grids using the geometrical convergence of solutions and the uniform convergence of subsolutions.展开更多
文摘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.
文摘In account of the famous Cebysev inequality, a rich theory has appeared in the literature. We establish some new weighted Cebysev type integral inequalities. Our proofs are of independent interest and provide new estimates on these types of inequalities.
文摘The Schwarz method for a class of elliptic variational inequalities with noncoercive operator was studied in this work. The author proved the error estimate in L∞-norm for two domains with overlapping nonmatching grids using the geometrical convergence of solutions and the uniform convergence of subsolutions.
基金Supported by the Natural Science Research Foundation of Science and Technology Bureau of Bijie Area(2008-06)The Natural Science Research Foudation of Guizhou Province Education Department(2008072)
