Mihalis Mourgoglou

Ikerbasque Research Associate, UPV/EHU

Department of Mathematics at the University of the Basque Country, UPV/EHU.

Research line:

Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory.

Previous research experience at Université Paris-Sud 11, Orsay (France), Institut des hautes études scientifiques (IHES), Bures-sur-Yvette, (France), Centre de Recerca Matemàtica (CRM) and Universitat Autònoma de Barcelona - UAB, (Spain).

Doctor in Mathematics (2011) fom the University of Missouri-Columbia (USA).

Argitalpenak
Kongresuak eta Proceedings

2023

Article / Quantitative differentiability on uniformly rectifiable sets and applications to Sobolev trace theorems

J. Azzam, M. Mourgoglou, and M. Villa

Article / Extrapolation of solvability of the regularity and the Poisson regularity problems in rough domains

J. M. Gallegos, M. Mourgoglou, and X. Tolsa

Article / Varopoulos' extensions of boundary functions in $L^p$ and $BMO$ in domains with Ahlfors-regular boundaries and applications

M. Mourgoglou and Th. Zacharopoulos

Article / Uniform Rectifiability, Elliptic Measure, Square Functions, and ϵ-Approximability Via an ACF Monotonicity Formula

International Mathematics Research Notices

Azzam, J.; Garnett, J.; Mourgoglou, M.; Tolsa, X.

Article / L2 -Boundedness of Gradients of Single Layer Potentials for Elliptic Operators with Coefficients of Dini Mean Oscillation-Type

Archive for Rational Mechanics and Analysis

Molero, A.; Mourgoglou, M.; Puliatti, C.; Tolsa, X.

Article / Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains

Calculus of Variations and Partial Differential Equations

Mourgoglou, M.

2022

Article / Solvability of the Poisson-Dirichlet problem with interior data in Lp′-Carleson spaces and its applications to the Lp-regularity problem

Preprint

M. Mourgoglou, B. Poggi, and X. Tolsa

Article / On the density problem in the parabolic space

Preprint

A. Merlo, M. Mourgoglou, and C. Pouliatti

2021

Article / Uniform rectifiability, elliptic measure, square functions, and ε-approximability via an ACF monotonicity formula

Int. Math. Res. Not.

Jonas Azzam, John Garnett, Mihalis Mourgoglou, and Xavier Tolsa

Article / Blow-ups of caloric measure in time varying domains and applications to two-phase problems

J. Math. Pures Appl.

M. Mourgoglou and C. Puliatti

Article / The regularity problem for the Laplace equation in rough domains

ArXiv Preprint

Mihalis Mourgoglou and Xavier Tolsa

Article / L2-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type

ArXiv Preprint

Alejandro Molero, Mihalis Mourgoglou, Carmelo Puliatti, and Xavier Tolsa

Article / Blow-ups of caloric measure in time varying domains and applications to two-phase problems

Journal des Mathematiques Pures et Appliquees

Mourgoglou, M.; Puliatti, C.

Article / A new approach to non-homogeneous local Tb theorems

Journal d'Analyse Mathematique

Martikainen, H.; Mourgoglou, M.; Vuorinen, E.

Article / Approximate tangents, harmonic measure, and domains with rectifiable boundaries

Proceedings of the American Mathematical Society

Mourgoglou, M.

2020

Article / Harmonic measure and quantitative connectivity: geometric characterization of the Lp -solvability of the Dirichlet problem

Inventiones Mathematicae

Azzam, J.; Hofmann, S.; Martell, J.M.; Mourgoglou, M.; Tolsa, X.

Article / A two-phase free boundary problem for harmonic measure and uniform rectifiability

Transactions of the American Mathematical Society

Azzam, J.; Mourgoglou, M.; Tolsa, X.

2019

Article / On a two-phase problem for harmonic measure in general domains

American Journal of Mathematics

Azzam, J.; Mourgoglou, M.; Tolsa, X.; Volberg, A.

Article / On Harmonic Measure and Rectifiability in Uniform Domains

Journal of Geometric Analysis

Mourgoglou, M.

Article / Absolute continuity of harmonic measure for domains with lower regular boundaries

Advances in Mathematics

Akman, M.; Azzam, J.; Mourgoglou, M.

Article / Failure of L 2 boundedness of gradients of single layer potentials for measures with zero low density

Mathematische Annalen

Conde-Alonso, J.M.; Mourgoglou, M.; Tolsa, X.

Article / Tangent measures of elliptic measure and applications

Analysis and PDE

Azzam, J.; Mourgoglou, M.

Article / Representation and uniqueness for boundary value elliptic problems via first order systems

Revista Matematica Iberoamericana

Auscher, P.; Mourgoglou, M.

2018

Article / Improved Cotlar's inequality in the context of local Tb theorems

Journal of Functional Analysis

Martikainen, H.; Mourgoglou, M.; Tolsa, X.

Article / Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions

Duke Mathematical Journal

Garnett, J.; Mourgoglou, M.; Tolsa, X.

2017

Article / Singular Sets for Harmonic Measure on Locally Flat Domains with Locally Finite Surface Measure

Int. Math. Res. Not.

J. Azzam, M. Mourgoglou, and X. Tolsa

2023

Conference organization | Harmonic Analysis, Partial Differential Equations, and Geometric Measure Theory in Bilbao 2023

international Conference "Harmonic Analysis, Partial Differential Equations, and Geometric Measure Theory in Bilbao 2023" - Conference organization

S. Hofmann, A. Merlo, M. Mourgoglou, C. Puliatti

Invited talk | Varopoulos' type extensions and applications to the solvability of Boundary Value Problems for second order elliptic operators in rough domains

Analysis Seminar - Invited talk

M. Mourgoglou

Invited talk | The Dirichlet problem with boundary data in Sobolev space for second order elliptic operators in rough domains

Analysis Seminar - Invited talk

M. Mourgoglou

2022

Invited talk | The regularity problems for the Laplace equation in rough domains

Workshop on “Harmonic Analysis, Singular Integrals, and PDEs” - Invited talk

Mihalis Mourgoglou

Invited talk | The regularity problems for the Laplace equation in rough domains

International Conference “Harmonic Analysis and PDE in Seoul”, 16/05-20/05/2022 - Invited talk

Mihalis Mourgoglou

Invited talk | The regularity problems for the Laplace equation in rough domains

Second Congress of Greek Mathematicians, SCGM-2022 July 4-8, 2022, - Invited talk

Mihalis Mourgoglou

Invited talk | The regularity problems for the Laplace equation in rough domains

Analysis Seminar - Invited talk

Mihalis Mourgoglou

2021

Invited talk | Blow-ups of Caloric measure in time-varying domains and applications to two-phase problems.

Greek Mathematical Seminar - Invited talk

Mihalis Mourgoglou and Carmelo Puliatti

Invited talk | The regularity problem for the Laplace equation in rough domains

Seminario de Análisis y Aplicaciones - Invited talk

Mihalis Mourgoglou and Xavier Tolsa

Invited talk | The regularity problem for the Laplace equation in rough domains

Seminari d' Análisi de Barcelona - Invited talk

Mihalis Mourgoglou and Xavier Tolsa

2020

Invited talk | Tangent measures of caloric measure and applications to two-phase free boundary problems

Analysis Meeting in memory of Pr. Michel Marias - Invited talk

M. Mourgoglou

2019

Conference organization | Fourth Summer School on Harmonic Analysis and Partial Differential Equations

P. Caro, M. Mourgoglou, I. Parissis and L. Roncal

Conference organization | International Conference on Harmonic Analysis and PDEs, University of Helsinki, 3-7 June 2019, Helsinki, Finland.

International Conference on Harmonic Analysis and PDEs - Conference organization

F. Di Plinio, H. Martikainen, adn M. Mourgoglou

Invited talk | Regularity theory and Green's function for elliptic PDE of second order with lower order terms in unbounded domains

Analysis Seminar - Invited talk

M. Mourgoglou

2017

Invited talk | Harmonic measure, Riesz transform, and rectifiability.

Third Summer School on Harmonic Analysis and Partial Differential Equations, July 10-14 2017 - Invited talk

Mihalis Mourgoglou

Invited talk | On a two-phase problem for harmonic measure

Meeting of the Royal Spanish Mathematical Society (RSME), 30/01 to 03/02/2017, Special Session in Harmonic Analysis - Invited talk

Mihalis Mourgoglou

Invited talk | E-approximability, Carleson estimates for bounded harmonic functions and uniform rectifiability

Analysis day in Logroño, 23-24/02/2017 - Invited talk

Mihalis Mourgoglou

Invited talk | A PDE characterization of uniform rectifiability

Analysis Meeting, 21-22 December 2017 - Invited talk

Mihalis Mourgoglou

Invited talk | Free boundary problems for harmonic measure and uniform rectifiability

Barcelona Analysis Seminar, 04/12/2017 - Invited talk

Mihalis Mourgoglou