K. Gkikas

activity

20122025

most citedSemilinear elliptic Schrödinger equations with singular potentials and absorption terms

3 citations · 10 across the 19 of their papers we have counts for

collaborators

20 papers

math.AP2025

Elliptic Schrödinger equations with gradient-dependent nonlinearity and Hardy potential singular on manifolds

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $Σ \subset Ω$ is a $C^{2}$ compact boundaryless submanifold in $R^{N}$ of dimension $k$ , $0 \leq k < N - 2$ .…

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.AP2024

Semilinear Schrödinger equations with Hardy potentials involving the distance to a boundary submanifold and gradient source nonlinearities

Konstantinos T. Gkikas, Miltiadis Paschalis

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a bounded $C^{2}$ domain and $Σ \subset \partial Ω$ be a compact $C^{2}$ submanifold of dimension $k$ . Denote the distance from $Σ$ by $d_{Σ}$ . In…

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★ 3 cited

Semilinear elliptic equations involving power nonlinearities and hardy potentials with boundary singularities

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $Σ \subset \partial Ω$ be a $C^{2}$ compact submanifold without boundary, of dimension $k$ , $0 \leq k \leq N - 1$ . We…

math.AP2022

Poisson Problems involving fractional Hardy operators and measures

H. Chen, K. T. Gkikas, P. T. Nguyen

In this paper, we study the Poisson problem involving a fractional Hardy operator and a measure source. The complex interplay between the nonlocal nature of the operator, the pecul…

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.AP2022★ 3 cited

Semilinear elliptic Schrödinger equations with singular potentials and absorption terms

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $Σ \subset Ω$ be a compact, $C^{2}$ submanifold without boundary, of dimension $k$ with $0 \leq k < N - 2$ . Put $L_…

math.AP2022

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N > 2$ ) be a $C^{2}$ bounded domain and $Σ \subset Ω$ be a compact, $C^{2}$ submanifold without boundary, of dimension $k$ with $0 \leq k < N - 2$ . Put $L_μ= Δ+…

math.AP2020

Green kernel and Martin kernel of Schrödinger operators with singular potential and application to the B.V.P. for linear elliptic equations

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $K \subset Ω$ be a compact, $C^{2}$ submanifold in $R^{N}$ without boundary, of dimension $k$ with $0\le…

math.AP2019

Semilinear elliptic equations with Hardy potential and gradient nonlinearity

Konstantinos Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a $C^{2}$ bounded domain and $δ$ be the distance to $\partial Ω$ . We study positive solutions of equation (E) $- L_{μ} u + g (∣\nabla u ∣) = 0$ …

math.AP2018

Optimal non-homogeneous improvements for the series expansion of Hardy's inequality

Konstantinos T. Gkikas, Georgios Psaradakis

We consider the series expansion of the $L^{p}$ -Hardy inequality of \cite{BFT2}, in the particular case where the distance is taken from an interior point of a bounded domain in $\ma…

math.AP2017

Ancient shrinking spherical interfaces in the Allen-Cahn flow

Manuel del Pino, Konstantinos T. Gkikas

We consider the parabolic Allen-Cahn equation in $R^{n}$ , $n \geq 2$ , $u_{t} = Δ u + (1 - u^{2}) u in R^{n} \times (- \infty, 0] .$ We construct an ancient radial…

math.AP2017★ 2 cited

Ancient multiple-layer solutions to the Allen-Cahn equation

Manuel del Pino, Konstantinos T. Gkikas

We consider the parabolic one-dimensional Allen-Cahn equation $u_{t} = u_{xx} + u (1 - u^{2}) (x, t) \in R \times (- \infty, 0] .$ The steady state $w (x) = tanh (x / 2)$ , co…

math.AP2016

On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

Let $Ω \subset R^{N}$ ( $N \geq 3$ ) be a bounded smooth domain and $δ (x) = dist (x, \partial Ω)$ . In this paper, we provide various necessary and sufficient conditions for…

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…

math.AP2013★ 2 cited

Classification of positive solutions of heat equation with supercritical absorption

Konstantinos Gkikas, Laurent Veron

Let $q \geq 1 + \frac{2}{N}$ . We prove that any positive solution of (E) $\prt_t u-\xD u+u^q=0$ in $R^{N} \times (0, \infty)$ admits an initial trace which is a nonnegative Borel…

math.AP2012

Initial value problems for diffusion equations with singular potential

Konstantinos Gkikas, Laurent Veron

Let $V$ be a nonnegative locally bounded function defined in $Q_\infty:=\BBR^n\times(0,\infty)$. We study under what conditions on $V$ and on a Radon measure $\gm$ in $\mathbb{R}^d…