In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q whi...In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.展开更多
Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in seve...Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in several space dimensions.展开更多
In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates ...In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates and the inverse function theorem.展开更多
文摘In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.
文摘Through the estimates for Greens function of linearized system, we obtain L p estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier Stokes systems of compressible flow in several space dimensions.
文摘In this paper, a semilinear elliptic-parabolic PDE system which arises in a two dimensional groundwater flow problem is studied. Existence and uniqueness results are established via the L￣p - L￣q a priori estimates and the inverse function theorem.
基金supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905)Shang hai Leading Academic Discipline Project (Grant No. J50101)+3 种基金Key Disciplines of Shanghai Municipality (GrantNo. S30104)Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700)National Natural Science Foundation of China (Grant No. 60532080)the Key Project of Chinese Ministryof Education (Grant No. 306017)
文摘In this paper we obtain local Lp estimates for the parabolic polyharmonic equations by a straightforward approach.
