This paper is concerned with partial regularity for weak solutions to nonlinear sub-elliptic systems related to Hörmander’s vector fields. The method of A-harmonic approximation introduced by Simon and developed by Duzaar and Grotowski is adapted to our context, and then a Caccioppoli-type inequality and partial regularity with optimal local Hölder exponent for gradients of weak solutions to th...

Abstract. In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Hölder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are i...

We study the boundedness of Riesz transforms in L for p > 2 on a doubling metric measure space endowed with a gradient operator and an injective, ω-accretive operator L satisfying Davies-Gaffney estimates. If L is non-negative self-adjoint, we show that under a reverse Hölder inequality, the Riesz transform is always bounded on L for p in some interval [2, 2 + ε), and that L gradient estimates ...

This manuscript develops the study of reverse Hilbert-type inequalities by applying Hölder on T. We generalize inequality with power two replacing a new β,β>1. The main results are proved using Specht’s ratio, chain rule and Jensen’s inequality. Our (when T=N) essentially new. Symmetrical properties play an essential role in determining correct methods to solve inequalities.