Emmanouil Milakis
+357 22 892640
...
PROFESSOR
Department of Mathematics and Statistics
FST 02 - Faculty of Pure and Applied Sciences, 062
University Campus
Education:
Ph.D. 2006 in Applied Mathematics, University of Crete, GREECE.
M.Sc. 2001 in Mathematics, University of Crete, GREECE.
B.Sc. 1999 in Mathematics, University of Crete, GREECE.
M.Sc. 2001 in Mathematics, University of Crete, GREECE.
B.Sc. 1999 in Mathematics, University of Crete, GREECE.
Academic Positions:
2023- University of Cyprus, Professor
2018-2023 University of Cyprus, Associate Professor
2013-2018 University of Cyprus, Assistant Professor
2009-2013 University of Cyprus, Lecturer (Tenure Track)
2006-2009 University of Washington, Acting Assistant Professor
2004-2005 University of Texas, Research Assistant.
2006-2009 University of Washington, Acting Assistant Professor
2004-2005 University of Texas, Research Assistant.
Partial Differential Equations.
Free Boundary Problems.
Geometric Measure Theory.
Free Boundary Problems.
Geometric Measure Theory.
- The Two-Phase Stefan problem with Anomalous Diffusion, (with I. Athanasopoulos and L. Caffarelli) Advances in Math. 406 (2022) 108527.
- The calibration method for the Thermal Insulation Functional, (with C. Labourie). ESAIM: Control, Optimisation & Calculus of Variations (2022).
- Higher Integrability of the gradient for the Thermal Insulation Problem, (with C. Labourie). Interfaces & Free Boundaries (2022).
- Regularity for Fully Nonlinear Parabolic Equations with Oblique Boundary Data (with G. Chatzigeorgiou). Rev. Mat. Iberoam. 37 (2021), 2, 775-820
- Parabolic Obstacle Problems. Quasi-convexity Regularity, (with I. Athanasopoulos and L. Caffarelli). Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (2019) Vol XIX 1-45.
- On the regularity of the Non-dynamic Fractional Obstacle Problem, (with I. Athanasopoulos and L. Caffarelli). J. Differential Equations (2018), 265, no 6, 2614-2647.
- Perturbations of Elliptic Operators in Chord Arc Domains. (with J. Pipher and T. Toro) Contemporary Math. 612 (2014), 143--161.
- Harmonic Analysis on Chord Arc Domains. (with J. Pipher and T. Toro) J. Geom. Anal. 23 (2013), no. 4, 2091--2157.
- On the extension property of Reifenberg-flat domains (with A. Lemenant and L. Spinolo) Ann. Acad. Sci. Fenn. Math., 39 (2014), no 1. 51-71.
- Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains (with A. Lemenant and L. Spinolo) Journal of Functional Analysis, 264 (2013), pp. 2097--2135.
- A stability result for nonlinear Neumann problems in Reifenberg flat domains in $mathbb{R}^{N}$. (with A. Lemenant) Publicacions Matem'{a}tiques 55 (2011), no. 2, 413--432.
- Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in $mathbb{R}^N$. (with A. Lemenant) J. Math. Anal. Appl. 364 (2010), pp. 522-533.
- Divergence form operators in Reifenberg flat domains. (with T. Toro) Mathematische Zeitschrift 264 (2010), no. 1, 15--41.
- Fully nonlinear phase transition problems with flat free boundaries. Differential Integral Equations 23 (2010), no. 1-2, 93--112.
- Optimal regularity in lower dimensional obstacle problems with variable coefficients. Unpublished manuscript (2009), available upon request.
- Regularity for the nonlinear Signorini problem (with L. Silvestre) Advances in Math. 217 (2008), 1301--1312.
- Regularity for fully nonlinear elliptic equations with Neumann boundary data (with L. Silvestre) Comm. Partial Differential Equations 31 (2006), no. 7-9, 1227--1252.
- On the regularity of optimal sets in mass transfer problems, Comm. Partial Differential Equations 31 (2006), no. 4-6, 817--826.
- Lipschitz regularity of viscosity solutions in some nonlinear parabolic-free boundary problems, Differential & difference equations and applications, (2006), 787--793.
- Two-phase transition problems for fully nonlinear parabolic equations of second order, Indiana Univ. Math. J. 54 No. 6 (2005), 1751--1770.
- Boundary Value Problems for Quasilinear Second Order Ordinary Differential equations, Nonlinear Analysis TMA 60 (2005) 149-162.