We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let the order of the equation approach two, we recover the theorem of Evans and Krylov about the regularity of solutions to concave uniformly elliptic partial differential equations.

the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

We consider the perturbation of parabolic operators of the form ∂t + P (x,D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseu...

1. The stationary, irrotational flow of a compressible fluid is characterized by a quasi-linear second order partial differential equation with coefficients which are functions of the first derivatives. The equation is sometimes elliptic and sometimes hyperbolic, depending on the magnitude of these first derivatives. The question of the existence of such flows satisfying prescribed conditions i...

in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact travel-ing wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general improved KdV (GIKdV) equation and Rðm; nÞ e...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...