Iteration, Inequalities, and Differentiability in Analog Computers

Iteration , Inequalities , and Di erentiabilityin Analog ComputersManuel

Some new variants of interval-valued Gronwall type inequalities on time scales

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.

Boundedness and pointwise differentiability of weak solutions to quasi-linear elliptic differential equations and variational inequalities

The local boundedness of weak solutions to variational inequalities (obstacle problem) with the linear growth condition is obtained. Consequently, an analogue of a theorem by Reshetnyak about a.e. differentiability of weak solutions to elliptic divergence type differential equations is proved for variational inequalities.

Differentiability of Solutions for the Non-degenerate P-laplacian in the Heisenberg Group

We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.

A bundle-type auxiliary problem method for solving generalized variational-like inequalities

For generalized variational-like inequalities, by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization, we present an implementable iterative method. To make the subproblem easier to solve, even though the preinvex function may not be convex, we still consider using the model similar to the one in [R. Mifflin, A modification and extension of Lema...