In this paper we consider Lipschitz graphs of functions which are stationary points strictly polyconvex energies. Such can be thought as integral currents, resp. varifolds, for some elliptic integrands. The regularity theory the latter is a widely open problem, in particular no counterpart classical Allard’s theorem known. We address issue from point view differential inclusions and show that r...

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

*Correspondence: [email protected] Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, P.R. China Abstract This paper is concerned with fractional differential inclusions with three-point fractional integral boundary conditions. We consider the fractional differential inclusions under both convexity and nonconvexity conditions on the multivalued term. Some new existenc...

The main purpose of the present paper is to impose onesided Lipschitz condition for differential inclusions on a closed and convex domain of a uniformly convex Banach space. Both differential inclusions with almost upper demicontinuous and almost lower semicontinuous right–hand sides are considered. The existence theorems are proved and it is shown that the set of solutions is connected. AMS Ma...

The paper provides topological characterization for solution sets of differential inclusions with (not necessarily smooth) functional constraints in Banach spaces. The corresponding compactness and tangency conditions for the right hand-side are expressed in terms of the measure of noncompactness and the Clarke generalized gradient, respectively. The consequences of the obtained result generali...