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:

[19] S. Creo, M. Hinz, M. R. Lancia, Non-local boundary energy forms for quasidiscs: Codimension gap and approximation, under review. Available on arXiv: https://arxiv.org/abs/2310.04549

 

[18] S. Creo, M. R. Lancia, G. Mola, S. Romanelli, Inverse problems in irregular domains: approximation via Mosco convergence, accepted for publication on Contemporary Mathematics.

 

[17] S. Creo, M. R. Lancia, Dynamic boundary conditions for time dependent fractional operators on extension domains, Adv. Differential Equations, 29 (9/10), (2024), 727-756.

 

[16] S. Creo, M. R. Lancia, The p-curl system in extension domains, Discrete Cont. Dyn. Syst. Series S, 17 (5&6), (2024), 2208-2223.

 

[15] R. Capitanelli, S. Creo, M. R. Lancia, Asymptotics for time-fractional Venttsel' problems in fractal domains, Fractal Fract., 7 (6), (2023), 479.

 

[14] M. Cefalo, S. Creo, M. R. Lancia, J. Rodriguez-Cuadrado, Fractal mixtures for optimal heat draining, Chaos Solitons Fractals, 173, (2023), paper no. 113750, 11 pp.

 

[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. Vιlez-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.