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This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
In this article, we first give the representation of solutions for the oblique derivative boundary value problem of generalized Lavrent 0 ev-Bitsadze equations including the Lavrent 0 ev-Bitsadz...
n this article, we discuss that an initial-irregular oblique derivative problem for non-linear uniformly parabolic complex equation of second order A0 u zˉ z −Re[Quzz+A1 u z ]−A2 u&...
n this article, we discuss the approximate method of solving irregular oblique derivative problem for nonlinear uniformly elliptic equation of second order u z1 z =F(z; u; u z ; u zz ) in D; (0...
In this article, we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order wz1z=F(z; w; w z ;wz; w zz ;wzz)+G(z; w; ; w z ;...
In this article, we discuss that an initial-oblique derivative boundary value problem for nonlinear uniformly parabolic complex equation of second order A0 u z1z¡Re[Quzz+A1 u z ]¡ ^ ...
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
In the paper, the Bismut derivative formula is established for multidimensional SDEs driven by additive fractional noise ($1/2reover the Harnack inequality is given. Through a Lamperti t...
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the...
Abstract: We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.
Abstract: For the higher order derivative(with respect to the first variable) of Hurwitz zeta function,we discuss as a function of the second variable,the location and the nature of its singularities ...
Abstract: We give a maximum principle proof of interior derivative estimates for the K\"ahler-Ricci flow, assuming local uniform bounds on the metric.
Abstract: We consider probability measures supported on a finite discrete interval $[0,n]$. We introduce a new finitedifference operator $\nabla_n$, defined as a linear combination of left and right f...
Abstract: By using the Malliavin calculus and solving a control problem, Bismut type derivative formulae are established for a class of degenerate diffusion semigroups with non-linear drifts. As appli...
Using the Gabor frame, we get some time-global dispersive estimates for the Schr¨odinger semi-group in anisotropic Lebesgue spaces, which include a time-global maximal function estimate in the space L...

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