We prove local weighted integral inequalities for differential forms. Then by using the local results, we prove global weighted integral inequalities for differential forms in L^s(μ)-averaging domains and in John dom...We prove local weighted integral inequalities for differential forms. Then by using the local results, we prove global weighted integral inequalities for differential forms in L^s(μ)-averaging domains and in John domains, respectively, which can be considered as generalizations of the classical Poincare-type inequality.展开更多
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus ...For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.展开更多
文摘We prove local weighted integral inequalities for differential forms. Then by using the local results, we prove global weighted integral inequalities for differential forms in L^s(μ)-averaging domains and in John domains, respectively, which can be considered as generalizations of the classical Poincare-type inequality.
文摘We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^(p) provided that the kernels satisfy weak conditions.
基金Supported by the Major State Basic Research Program of China (No. 1999032803)the National Tackling Key Problems Program (No. 2002020094)+1 种基金the National Natural Scicnccs Foundation of China (Nos.19972039,10271066)the Doctorate Foundation of the Ministry of Education of China (No.2003042047)
文摘For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L^2 norm are derived for the error in the approximate solution.
