Modulus of continuity of solutions to complex Hessian equations

Boundary Continuity of Solutions to Elliptic Equations with Nonstandard Growth

We study regularity properties of weak solutions to elliptic equations involving variable growth exponents. We prove the sufficiency of a Wiener type criterion for the regularity of boundary points. This criterion is formulated in terms of the natural capacity involving the variable growth exponent. We also prove the Hölder continuity of weak solutions up to the boundary in domains with uniform...

Continuity properties of solutions to H2 and H∞ Riccati equations

In most H2 and H∞ control problems solutions of the algebraic Riccati equation play a crucial role. Note that in general for continuous time systems we have to use quadratic matrix inequalities instead of Riccati equations. For details we refer to [5]. In particular we are interested in the stabilizing solution of these Riccati equations and quadratic matrix inequalities. However, if the system...

Continuity Properties of Solutions to Some Degenerate Elliptic Equations

We consider a nonlinear (possibly) degenerate elliptic operator Lv = − div a(∇v) + b(x, v) where the functions a and b are, unnecessarly strictly, monotonic. For a given boundary datum φ we prove the existence of the maximum and the minimum of the solutions and formulate a Haar-Rado type result, namely a continuity property for these solutions that may follow from the continuity of φ. In the ho...

On genuine Lupac{s}-Beta operators and modulus of continuity

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

Modulus of continuity on parts of the boundary and solid modulus of continuity