Georgios Sakellaris

Georgios Sakellaris obtained his Bachelor in Mathematics from the University of Athens, Greece, in June 2011. He continued his studies at the University of Chicago, from which he obtained his Master in June 2013, and his PhD in June 2017, under the supervision of Professor Carlos Kenig.

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Georgios Sakellaris' research lies in the field of partial differential equations. One direction that he is interested in is boundary value problems for second order elliptic equations with lower order coefficients in Lipschitz domains, in the case that the boundary data is not necessarily continuous. Some instances include the D_2 Dirichlet problem in the case that the data is square integrable on the boundary, and the R_2 Regularity problem when both the data and its tangential derivative are square integrable.
 
Another direction of research is the construction of Green's function for equations with lower order coefficients, in settings that are subcritical or scale invariant. In this direction, he has been investigating the effect that the lower order coefficients have in obtaining pointwise bounds and weak-type bounds for Green's function, in domains with little or no regularity.
 
Finally, he has lately been interested in free boundary problems involving the fractional Laplacian.

PUBLICATIONS WITHIN THE P-SPHERE PROJECT

• Seick Kim and Georgios Sakellaris, Green's function for second order elliptic equations with singular lower order coefficients, Communications in Partial Differential Equations (2018), 1-43.

Conferences attended:

• October 2018: PDEs and Geometric Measure Theory, ETH, Zurich.

• July 2018: Geometric Function Theory in Fluid Dynamics, Barcelona.

• June 2018: Geometric Measure Theory and its Connections, Helsinki, Finland.

• May 2018: Workshop on Real Harmonic Analysis and its Applications to Partial Differential Equations and Geometric Measure Theory, ICMAT, Madrid

• May 2018: School on Real Harmonic Analysis and its Applications to Partial Differential Equations and Geometric Measure Theory, ICMAT, Madrid.

• April 2018: Harmonic Analysis of Elliptic and Parabolic Partial Differential Equations, CIRM, Marseille, France.

• October 2017: Harmonic Analysis and Geometric Measure Theory, CIRM, Marseille, France.

• June 2015: Second Chicago Summer School In Analysis, University of Chicago.

• September 2014: Harmonic Analysis & Partial Differential Equations: Recent Developments & Future Directions, University of Chicago.

•  June 2014: First Chicago Summer School In Analysis, University of Chicago.