Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong＇s class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is pres...Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong＇s class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the Bp weight properties for the solution u near the boundary.展开更多
Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA...Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA,α from the central Morrey spaces E^p,μ1 to E^r,λ for λ = μ1 ＋ μ2 ＋ α/n and 1/r = 1/p ＋ 1/q - α/n.展开更多
基金supported by National Nature of Science Foundation of China(No.10471069)by Natural Science Foundation of Zhejiang province of China(No.102066)by NSF of Ningbo city(No.2006A610090)
文摘Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato-Fefferman-Phong＇s class in Lipschitz domains. An elementary proof of the doubling property for u^2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the Bp weight properties for the solution u near the boundary.
基金supported by National Natural Science Foundation of China(Grant Nos.11226104 and 11226109)supported by National Natural Science Foundation of China(Grant Nos.11171306 and 11071065)Natural Science Foundation of Jiangxi Province(Grant No.20114BAB211007)
文摘Let 0 〈 a 〈 n, Ω be a rough kernel, and let A have derivatives of order m- 1 in CI3MOTM with m ≥ 2. We consider a class of generalized commutators TΩA,α of Cohen-Gosselin type, and obtain the boundedness of TΩA,α from the central Morrey spaces E^p,μ1 to E^r,λ for λ = μ1 ＋ μ2 ＋ α/n and 1/r = 1/p ＋ 1/q - α/n.
