Research interests

Research topics: Boundary Value Problems in irregular domains (fractals, (epsilon,delta), d-sets).

a) Linear and quasilinear Venttsel’ problems on pre-fractal and fractal domains:

1. Existence, uniqueness and regularity of the weak solutions;

2. Asymptotic behavior of the solutions;

3. Numerical approximation of Venttsel’ problems in pre-fractal domains.

b) Robin-Venttsel’ problems for (nonlinear) fractional operators on pre-fractal and fractal domains:

1. Existence, uniqueness and regularity of the weak solutions;

2. Asymptotic behavior of the solutions.

c) Problems of mathematical physics on pre-fractal and fractal domains:

1. Magnetostatic problems;

2. Stokes problems;

3. Compactness properties of magnetic operators (Friedrichs and Gaffney inequalities).

Papers and other products:

[15] S. Creo, M. R. Lancia, Dynamical boundary conditions for time-dependent fractional operators on extension domains, under review. Available on arXiv: https://arxiv.org/abs/2205.06656

[14] S. Creo, M. R. Lancia, The p-curl system in extension domains, under review.

[13] S. Creo, M. R. Lancia, P. Vernole, Transmission problems for the fractional p-Laplacian across fractal interfaces, Discrete Cont. Dyn. Syst. Series S, 15 (12), (2022), 3621-3644.

[12] S. Creo, Singular p-homogenization for highly conductive fractal layers, Z. Anal. Anwendungen, 40 (4), (2021), 401-424.

[11] S. Creo, M. R. Lancia, Fractional (s,p)-Robin-Venttsel’ problems on extension domains, NoDEA Nonlinear Differential Equations Appl., 28 (3), (2021), paper no. 31, 33 pp.

[10] M. Cefalo, S. Creo, M. Gallo, M. R. Lancia, P. Vernole, Approximation of 3D Stokes flows in fractal domains, in: Fractals in Engineering: Theoretical Aspects and Numerical Approximation, SEMA SIMAI Springer Series vol. 8, Spinger-Cham, (2021), 27-53.

[9] S. Creo, M. R. Lancia, P. Vernole, M-Convergence of p-fractional energies in irregular domains, J. Convex Analysis, 28 (2), (2021), 509-534.

[8] S. Creo, M. R. Lancia, A. I. Nazarov, Regularity results for nonlocal evolution Venttsel’ problems, Fract. Calc. Appl. Anal., 23 (5), (2020), 1416-1430.

[7] S. Creo, M. Hinz, M. R. Lancia, A. Teplyaev, P. Vernole, Magnetostatic problems in fractal domains, in: Fractals and Dynamics for Mathematics, Science and the Arts, Volume 5: Analysis, Probability and Mathematical Physics on Fractals, World Scientific, (2020), 477-502.

[6] S. Creo, M. R. Lancia, Friedrichs inequality in irregular domains, J. Math. Anal. Appl., 484 (1), (2020), 123665.

[5] S. Creo, M. R. Lancia, P. Vernole, Convergence of fractional diffusion processes in extension domains, J. Evol. Equ., 20 (1), (2020), 109-139.

[4] M. Cefalo, S. Creo, M. R. Lancia, P. Vernole, Nonlocal Venttsel’ diffusion in fractal-type domains: regularity results and numerical approximation, Math. Methods Appl. Sci., 42 (14), (2019), 4712-4733.

[3] S. Creo, V. Regis Durante, Convergence and density results for parabolic quasi-linear Venttsel’ problems in fractal domains, Discrete Cont. Dyn. Syst. Series S, 12 (1), (2019), 65-90.

[2] S. Creo, M. R. Lancia, A. Nazarov, P. Vernole, On two-dimensional nonlocal Venttsel’ problems in piecewise smooth domains, Discrete Cont. Dyn. Syst. Series S, 12 (1), (2019), 57-64.

[1] S. Creo, M. R. Lancia, A. Vélez-Santiago, P. Vernole, Approximation of a nonlinear fractal energy functional on varying Hilbert spaces, Commun. Pure Appl. Anal., 17 (2), (2018), 647–669.

[*] S. Creo, Local and nonlocal Venttsel’ problems in fractal domains, PhD Thesis. Supervisor: Maria Rosaria Lancia.