In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the co...In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the conditionp> max {1, 2N N+2 }is determined by the behaviour of u . Theorem implies that for solution in L N loc (Ω T ), the condition for the gradient of solution being H o¨ lder continuous needs only p>1 .展开更多
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈...Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.展开更多
文摘In , Ho¨lder continuity for the spatial gradient of weak solutions ofu t= div(|u| p-2 u) in Ω T= Ω ×(0,T)was established, where = grad x, Ω R N . We discuss here how the conditionp> max {1, 2N N+2 }is determined by the behaviour of u . Theorem implies that for solution in L N loc (Ω T ), the condition for the gradient of solution being H o¨ lder continuous needs only p>1 .
基金National Natural Science Foundation of China (Grant Nos. 10901018 and 11001002)the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Fundamental Research Funds for the Central Universities
文摘Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.
