$L^2$-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.

Estimates of First and Second Order Shape Derivatives in Nonsmooth Multidimensional Domains and Applications

Second-order nonsmooth optimization for H ∞ synthesis

The standard way to compute H∞ feedback controllers uses algebraic Riccati equations and is therefore of limited applicability. Here we present a new approach to the H∞ output feedback control design problem, which is based on nonlinear and nonsmooth mathematical programming techniques. Our approach avoids the use of Lyapunov variables, and is therefore flexible in many practical situations.

On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Hölder Regularity of Solutions to Second-Order Elliptic Equations in Nonsmooth Domains

We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equations in domains satisfying an exterior cone condition, similar results were obtained by J. H. Michael, who in turn relied on the barrier techniques due to K. Miller. Our approach is based on...

Second-order Derivatives and Rearrangements

Inequality (1.2) is classical and very well known. It has been the object of extensions and variants which can be found in a number of papers and monographs, including [AFLT], [Bae], [BBMP], [BH], [Bro], [BZ], [CP], [E], [H], [Ka2], [Kl], [Ma], [Sp1], [Sp2], [Spi], [Ta1], [Ta5], and [Ta6]. Even if not as popular as (1.2), inequality (1.1) has also been known for a long time, and versions of it ...