Konstantinos T. Gkikas

RESEARCH PROJECTS (Principal Investigator)

18/11/2020-16/05/2024: Hellenic Foundation for Research and Innovation (H.F.R.I.) under the ”2nd Call for

H.F.R.I. Research Projects to support Post-Doctoral Researchers” (Project Number: 59).

Project title: ”Nonlinear Elliptic Problems With Hardy Type Potentials And Multiple-Layer Solutions To

Parabolic Allen-Cahn Equation”.

02/11/2013-31/10/2016: Programa FONDECYT CONICYT, No 3140567.

Sponsor Investigator: Prof. Manuel del Pino.

Project title: ”Singular solutions to nonlinear elliptic and parabolic equations”.

Publications and Preprints

(with H.Chen and P.-T. Nguyen) Semilinear elliptic equations involving fractional Hardy operators, submitted. (arxiv)

(with P.-T. Nguyen) Elliptic Schrödinger equations with gradient-dependent nonlinearity and Hardy potential singular on manifolds, J Geom Anal 35, 212 (2025). https://doi.org/10.1007/s12220-025-02046-9. (arxiv)

Ancient solutions to the Allen Cahn equation in catenoids, Asymptotic Analysis. 2025;0(0). doi:10.1177/09217134251344413. (arxiv)

(with M. Paschalis) Semilinear Schrödinger equations with Hardy potentials involving the distance to a boundary submanifold and gradient source nonlinearities. Nonlinear Differ. Equ. Appl. 32, 13 (2025).

Nonlinear nonlocal equations involving subcritical or power nonlinearities and measure data, Math. Eng. 2024, 6(1): 45-80. doi: 10.3934/mine.2024003 .(arxiv)

(with P.-T. Nguyen) Semilinear elliptic Schrödinger equations involving singular potentials and source terms, Nonlinear Anal. Volume 238 (2024). (arxiv)

(with P.-T. Nguyen) Semilinear elliptic Schrödinger equations with singular potentials and absorption terms, J. London Math. Soc., 109: e12844 (2024). https://doi.org/10.1112/jlms.12844. (arxiv)

(with P.-T. Nguyen) Semilinear elliptic equations involving power nonlinearities and Hardy potentials with boundary singularities, Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2023:1-58. https://doi:10.1017/prm.2023.122 (arxiv)

Quasilinear elliptic equations involving measure valued absorption terms and measure data, JAMA (2023). https://doi.org/10.1007/s11854-023-0321-0.

(with H.Chen and P.-T. Nguyen) Poisson Problems involving fractional Hardy operators and measures, Nonlinearity 36 (2023) 7191–7229. (arxiv)

(with G. Barbatis and A. Tertikas) Heat and Martin kernel estimates for Schrödinger operators with critical Hardy potentials, Math. Ann. (2023). https://doi.org/10.1007/s00208-023-02693-9. (arxiv)

(with P.-T. Nguyen) Martin kernel of Schrödinger operators with singular potential and application to the B.V.P. for linear elliptic equations, Calc. Var. (2022) 61:1. (arxiv)

(with G. Psaradakis) Optimal non-homogeneous improvements for the series expansion of Hardy’s inequality, Commun. Contemp. Math. 24 (8), 2150031, 2022. (arxiv)

(with P.-T. Nguyen) Elliptic equations with Hardy potential and gradient-dependent nonlinearity, Adv. Nonlinear Stud. 2020; 20(2): 399–435. (researchgate)

(with P.-T. Nguyen) Semilinear elliptic equations with Hardy potential and gradient nonlinearity, Rev. Mat. Iberoam. 36 (2020), no. 4, 1207–1256. (arxiv)

(with P.-T. Nguyen) On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials, J. Differential Equations 266 (2019), no. 1, 833-875. (arxiv)

(with L. Véron) The spherical p-harmonic eigenvalue problem in non-smooth domains, J. Funct. Anal. 274 (2018), no. 4, 1155-1176. (arxiv)

(with M. del Pino) Ancient shrinking spherical interfaces in the Allen-Cahn flow, Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 1, 187-215. (arxiv)

(with M. del Pino) Ancient multiple-layer solutions to the Allen-Cahn Equation, Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), no. 6, 1165-1199. (arxiv)

Boundary Singularities on a Wedge-like Domain of a Semilinear Elliptic Equation, Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 5, 979-1006. (arxiv)

(with L.Véron) Boundary singularities of solutions of semilinear elliptic equations with critical Hardy potentials, Nonlinear Anal. 121 (2015), 469-540. (arxiv)

(with L. Véron ) Measure boundary value problems for semilinear elliptic equations with critical Hardy potentials, C. R. Acad. Sci. Paris 353, 315-320 (2015). (arxiv)

(with L. Véron ) Complete classification of positive solutions of supercritical semilinear heat equations with absorption, Adv. Nonlinear Stud. 14 (2014), no. 1, 47-113. (arxiv)

(with L. Véron) Initial value problems for diffusion equations with singular potential, Contemp. Math. 594, 201-230, Amer. Math. Soc., Providence, RI (2013). (arxiv)

Hardy-Sobolev Inequalities in Unbounded Domains and Heat Kernel Estimates, J. Funct. Anal. 264 (2013), no. 3, 837-893.

Existence and Nonexistence of Energy Solutions for Linear Elliptic Equations Involving Hardy-type Potentials, Indiana Univ. Math. J. 58 No. 5 (2009), 2317-2345. (researchgate)