Nikolaos Roidos
Position:
Associate Professor
Address:
University of Patras
26504 Rio Patras
Greece
Contact:
roidos@math.upatras.gr
Research interests:
(AP) Linear and quasilinear parabolic problems on manifolds with singularities
(FA) Functional calculus for sectorial operators
(ST) Spectral theory and scattering theory of the Laplacian on manifolds with singularities
Publications:
Preprints
Strip-type operators and abstract Cauchy problems. [arXiv:2601.19075].
Asymptotics of solutions to the porous medium equation near conical singularities (with E. Schrohe). [arXiv:2503.02044].
Maximal Lq-regularity for the Laplacian on manifolds with edges. [arXiv:2310.12578].
Refereed papers
The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points. Semigroup Forum (to appear) [arXiv:2312.00573].
Curve shortening flow on Riemann surfaces with conical singularities (with A. Savas-Halilaj). Math. Ann. 390, 2337-2411 (2024). [arXiv:2007.01024].
Existence of global attractors and convergence of solutions for the Cahn-Hilliard equation on manifolds with conical singularities (with P. T. P. Lopes). J. Math. Anal. Appl. 531, no. 2, 127851 (2024). [arXiv:2201.12915].
Maximal Lq-regularity of nonlocal parabolic equations in higher order Bessel potential spaces (with Y. Shao). Pure Appl. Funct. Anal. 7, no. 3, 1037-1063 (2022). [arXiv:2103.16361].
Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation (with Y. Shao). Evol. Equ. and Control Theory 11, no. 3, 793-825 (2022). [arXiv:2009.06744].
The fractional porous medium equation on manifolds with conical singularities II (with Y. Shao). Math. Nachr. 296, no. 4, 1616-1650 (2023). [arXiv:1908.07138].
The fractional porous medium equation on manifolds with conical singularities I (with Y. Shao). J. Evol. Equ. 22, no. 1 (2022). [arXiv:1908.06915].
Bounded H∞-calculus for boundary value problems on manifolds with conical singularities (with E. Schrohe and J. Seiler). J. Differential Equations 297, 370-408 (2021). [arXiv:1906.03701].
Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities (with P. T. P. Lopes). Monatshefte für Mathematik 197, 677-716 (2022). [arXiv:1903.06628].
Heinz-Kato inequality in Banach spaces. J. Anal. 28, no. 3, 841-846 (2020). [arXiv:1811.04739].
Conic manifolds under the Yamabe flow. J. Evol. Equ. 20, no. 2, 321-334 (2020). [arXiv:1807.04139].
Expanding solutions of quasilinear parabolic equations. Comm. Pure Appl. Anal. 20, no. 4, 1413-1429 (2021). [arXiv:1712.09110].
Smoothness and long time existence for solutions of the porous medium equation on manifolds with conical singularities (with E. Schrohe). Comm. Partial Differential Equations 43, no. 10, 1456-1484 (2018). [arXiv:1708.07542].
Complex powers for cone differential operators and the heat equation on manifolds with conical singularities. Proceedings of the Amer. Math. Soc. 146, no. 7, 2995-3007 (2018). [arXiv:1702.00253].
The Swift-Hohenberg equation on conic manifolds. J. Math. Anal. Appl. 481, no. 2, 123491 (2020). [arXiv:1612.08766].
A scattering approach to a surface with hyperbolic cusp. Annales Henri Poincaré 19, no. 5, 1489-1505 (2018). [arXiv:1610.04625].
Closedness and invertibility for the sum of two closed operators. Adv. Oper. Theory 3, no. 3, 582-605 (2018). [arXiv:1602.04465].
Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities (with E. Schrohe). Comm. Partial Differential Equations 41, no. 9, 1441-1471 (2016). [arXiv:1504.05101].
Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation (with E. Schrohe). J. Differential Equations 257, no. 3, 611-637 (2014). [arXiv:1311.4702].
Preserving closedness of operators under summation. J. Funct. Anal. 266, no. 12, 6938-6953 (2014). [arXiv:1307.3462].
On the inverse of the sum of two sectorial operators. J. Funct. Anal. 265, no. 2, 208-222 (2013). [arXiv:1207.0749].
The Cahn-Hilliard equation and the Allen-Cahn equation on manifolds with conical singularities (with E. Schrohe). Comm. Partial Differential Equations 38, no. 5, 925-943 (2013). [arXiv:1203.3111].
Scattering theory of the p-form Laplacian on manifolds with generalized cusps (with E. Hunsicker and A. Strohmaier). J. Spectr. Theory 4, no. 1, 177-209 (2014). [arXiv:1106.3032].
Miscellaneous
On a staircase function. The Mathematical Gazette 107, no. 570, 501-503 (2023).
Analysis on manifolds with generalized cusps, spectral theory of the Laplace operator. Lambert Academic Publishing (2010).