In this paper we study predimension inequalities in differential fields and define what it means for such an inequality to be adequate . Adequacy was informally introduced by Zilber, here give a precise definition quite general context. We also discuss the connection of problem definability derivations reducts differentially closed fields. The Ax-Schanuel exponential equation (proved Ax) its an...

The aim of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with nonstandard initial inequalities with sums in relatively arbitrary (n+1)-dimensional time-space sets more general than the cylindrical domain.

In this article, we establish some integral inequalities for function with two independent variables. Also we show applications of these inequalities for finding bounds of solutions to partial differential equations.

The aim of the present paper is to establish some variants integral inequalities in two independent variables. These integral inequalities given here can be applied as tools in the boundedness and uniquness of certain partial differential equations.

This is a survey article for Surveys in Differential Geometry series on the subject of Li-Yau-Hamilton type differential inequalities and related monotonicity formulae.