Research

CONSEQUAT

CONSEQUAT

This research was sponsored, by the Marie Curie International Reintegration Grant “FBPsinSC” no. PIRG06-GA-2009-256481, NSF DMS grant 0856687,

European Regional Development Fund and the Republic of Cyprus through the Research and Innovation Foundation grand EXCELLENCE/1216/0025 and the University of Cyprus research grants.

[22] The Two-Phase Stefan problem with Anomalous Diffusion, (with I. Athanasopoulos and L. Caffarelli) 2021.


[21] The calibration method for the Thermal Insulation Functional, (with C. Labourie). Submitted (2021). ArXiv.


[20] Higher Integrability of the gradient for the Thermal Insulation Problem, (with C. Labourie). Submitted (2021). ArXiv.


[19] Regularity for Fully Nonlinear Parabolic Equations with Oblique Boundary Data, (with G. Chatzigeorgiou). Rev. Mat. Iberoam. 37 (2021),  2, 775-820.


[18] 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.


[17] 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.


[16] A Parabolic Almgren’s Monotonicity Formula for degenerate operators and applications, (with I. Athanasopoulos and L. Caffarelli). Preprint, 26 pages.


[15] Perturbations of elliptic operators in chord arc domains, (with J.

Pipher and T. Toro). Contemp Math. 612 (2014), pp. 143–161.


[14] 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.


[13] 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.


[12] Harmonic Analysis on Chord Arc Domains, (with J. Pipher and T.

Toro). J. Geom. Anal. 23 (2013), no. 4, 2091–2157.


[11] A stability result for nonlinear Neumann problems in Reifenberg flat domains in R^N, (with A. Lemenant). Publ. Mat. 55 (2011), no. 2,

413–432.


[10] Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in R^N, (with A. Lemenant). J. Math. Anal. Appl. 364 (2010), no. 2, 522–533.


[9] Divergence form operators in Reifenberg flat domains, (with T. Toro). Mathematische Zeitschrift 264 (2010), no. 1, 15–41.


[8] Fully nonlinear phase transition problems with flat free boundaries. Differential Integral Equations 23 (2010), no. 1-2, 93–112.


[7] Optimal regularity in lower dimensional obstacle problems with variable coefficients. Unpublished manuscript (2009), 22 pages.


[6] Regularity for the nonlinear Signorini problem, (with L. Silvestre).

Advances in Math. 217 (2008), 1301–1312.


[5] Regularity for fully nonlinear elliptic equations with Neumann boundary data, (with L. Silvestre). Comm. Partial Differential Equations 31 (2006), no. 4-6, 1227–1252.


[4] On the regularity of optimal sets in mass transfer problems, Comm.

Partial Differential Equations 31 (2006), no. 4-6, 817–826.


[3] Lipschitz regularity of viscosity solutions in some nonlinear parabolic free boundary problems. 787–793, Hindawi Publ. Corp., New York, 2006.


[2] Boundary Value Problems for Quasilinear Second Order Ordinary Differential equations, Nonlinear Analysis TMA 60 (2005) 149-162.


[1] Two-phase transition problems for fully nonlinear parabolic equations of second order, Indiana Univ. Math. J. 54 (2005), no. 6, 1751–1768.