Weighted Estimates of Variable Kernel Fractional Integral and Its Commutators on Vanishing Generalized Morrey Spaces with Variable Exponent

In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces.And the corresponding commutators generated by BMO function are also considered.

STRONG COMPARISON PRINCIPLES FOR SOME NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form △2ψ ＋ L（x,△ ψ）, including the conformal hessian operator.

Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds

In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.

On Fridman Invariants and Generalized Squeezing Functions

In this paper,the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions and Fridman invariants.They also study the comparison of these two invariants,in terms of the so-called quotient invariant.

Generalized Integral Representations for Functions with Values in C(V_(3,3))

By using the solution to the Helmholtz equation u-λu = 0(λ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.

Ricci-Bourguignon Flow on Manifolds with Boundary

The authors consider the short time existence for Ricci-Bourguignon flow on manifolds with boundary.If the initial metric has constant mean curvature and satisfies some compatibility conditions,they show the short time existence of the Ricci-Bourguignon flow with constant mean curvature on the boundary.