K. Gkikas

activity

20122022

most citedAncient multiple-layer solutions to the Allen-Cahn equation

2 citations · 2 across the 6 of their papers we have counts for

collaborators

7 papers

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…