Concavity properties of solutions to Robin problems

Concavity Properties for Free Boundary Elliptic Problems

We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn’s type inequality for the Bernoulli Constant and we study the behaviour of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior non-linear Bernoulli problem.

Concavity and B-concavity of Solutions of Quasilinear Filtration Equations

Common solutions to pseudomonotone equilibrium problems

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

Some concavity properties for general integral operators

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

On regularity properties of solutions to hysteresis-type problems

We consider equations with the simplest hysteresis operator at the right-hand side. Such equations describe the so-called processes ”with memory” in which various substances interact according to the hysteresis law. We present some results concerning the optimal regularity of solutions. Our arguments are based on quadratic growth estimates for solutions near the free boundary.