Konstantinos T. Gkikas

activity

20142024

collaborators

6 papers

math.AP2024

Ancient solutions to the Allen Cahn equation in catenoids

Konstantinos T. Gkikas

Let $N \geq 2$ and $F : R^{N} \to R$ be the unique increasing radially symmetric function satisfying the minimal surface equation for graphs with the initial condition…

math.AP2023

Nonlinear nonlocal equations involving subcritical or power nonlinearities and measure data

Konstantinos T. Gkikas

Let $s \in (0, 1),$ $1 < p < \frac{N}{s}$ and $Ω \subset R^{N}$ be an open bounded set. In this work we study the existence of solutions to problems ( $E_{\pm}$ ) $Lu \pm g (u) = μ$ and $u=0…

math.AP2023

Semilinear elliptic equations involving fractional Hardy operators

Huyuan Chen, Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Our aim in this article is to study semilinear elliptic equations involving a fractional Hardy operator, an absorption and a Radon source in a weighted distributional sense. We sho…

math.AP2022

Heat and Martin kernel estimates for Schrödinger operators with critical Hardy potentials

Gerassimos Barbatis, Konstantinos T. Gkikas, Achilles Tertikas

Let $Ω$ be a bounded domain in $R^{N}$ with $C^{2}$ boundary and let $K \subset \partial Ω$ be either a $C^{2}$ submanifold of the boundary of codimension $k < N$ or a point. In this…

math.AP2014

Boundary singularities of solutions of semilinear elliptic equations with critical Hardy potentials

Konstantinos T. Gkikas, Laurent Veron

We study the boundary behaviour of the of (E) $-\Gd u-\myfrac{\xk }{d^2(x)}u+g(u)=0$, where $0<\xk <\frac{1}{4}$ and $g$ is a continuous nonndecreasing function in a bounded convex…

math.AP2014

Measure boundary value problem for semilinear elliptic equations with critical Hardy potentials

Konstantinos Gkikas, Laurent Veron

Let $Ω\subset\BBR^N$ be a bounded $C^{2}$ domain and $\CL_\gk=-\Gd-\frac{\gk}{d^2}$ the Hardy operator where $d=\dist (.,\prt\Gw)$ and $0<\gk\leq\frac{1}{4}$. Let $\ga_{\pm}=1\pm\sqr…