Geometric Analysis and Potential Theory

Project Information

GAPT

Grant agreement ID: 101018680

DOI

10.3030/101018680

EC signature date 5 May 2021

Start date 1 June 2021

End date 31 May 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 476 000,00

EU contribution

€ 1 476 000,00

Coordinated by

UNIVERSITAT AUTONOMA DE BARCELONA
Spain

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (15)

The dimension of planar elliptic measures arising from Lipschitz matrices in Reifenberg flat domains

Author(s): Ignasi Guillén-Mola, Martí Prats, Xavier Tolsa
Published in: Analysis and Mathematical Physics, Issue 15, 2025, ISSN 1664-2368
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s13324-025-01067-5

The Dimension of Harmonic Measure on Some AD-Regular Flat Sets of Fractional Dimension

Author(s): Xavier Tolsa
Published in: International Mathematics Research Notices. IMRN, 2023, Page(s) Published electronically, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnad184

A counterexample regarding a two-phase problem for harmonic measure in VMO

Author(s): Xavier Tolsa
Published in: Potential Analysis, Issue 63 (2025), no. 3, 2025, Page(s) 1499–1515, ISSN 0926-2601
Publisher: Kluwer Academic Publishers
DOI: 10.21203/rs.3.rs-4095167/v1

Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields

Author(s): Bruno Poggi
Published in: Advances in Mathematics, Issue 445, 2024, Page(s) 109665, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2024.109665

Solvability of the Poisson–Dirichlet problem with interior data in $L^{p'}$-Carleson spaces and its applications to the $L^{p}$-regularity problem

Author(s): Mihalis Mourgoglou, Bruno Poggi, Xavier Tolsa
Published in: Journal of the European Mathematical Society, 2025, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1660

On an almost sharp Liouville type theorem for fractional Navier-Stokes equations

Author(s): Diego Chamorro, Bruno Poggi
Published in: Publicacions Matemàtiques, Issue 69, 2024, Page(s) 27-43, ISSN 0214-1493
Publisher: Universitat de Barcelona
DOI: 10.5565/publmat6912502

Ricci curvature bounded below and uniform rectifiability

Author(s): Matthew Hyde, Michele Villa, Ivan Yuri Violo
Published in: Annales Fennici Mathematici, Issue 49, 2024, ISSN 2737-114X
Publisher: Finnish Mathematical Society
DOI: 10.54330/afm.153338

Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant

Author(s): Gallegos, Josep M.
Published in: Calculus of Variations and Partial Differential Equations, 2023, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-022-02426-x

The two-phase problem for harmonic measure in VMO and the chord-arc condition

Author(s): Tolsa, Xavier; Toro, Tatiana
Published in: Trans. Amer. Math. Soc., 2024, Page(s) Accepted for publication, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.48550/arxiv.2209.14346

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

Author(s): Josep M. Gallegos, Mihalis Mourgoglou, Xavier Tolsa
Published in: Journal of Functional Analysis, Issue 288, 2024, Page(s) 110672, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2024.110672

The $A_\infty$ condition, $\varepsilon$-approximators, and Varopoulos extensions in uniform domains

Author(s): Bortz, Simon; Poggi, Bruno; Tapiola, Olli; Tolsa, Xavier
Published in: The Journal of Geometric Analysis, Issue 1, 2024, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-024-01666-x

The regularity problem for the Laplace equation in rough domains

Author(s): Mourgoglou, Mihalis; Tolsa, Xavier
Published in: Duke Mathematical Journal, 2023, Page(s) Accepted for publication, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.48550/arxiv.2110.02205

Carleson’s $\varepsilon ^{2}$ conjecture in higher dimensions

Author(s): Ian Fleschler, Xavier Tolsa, Michele Villa
Published in: Inventiones mathematicae, Issue 241, 2025, Page(s) 207-307, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-025-01337-w

Critical Perturbations for Second Order Elliptic Operators—Part II: Non-tangential Maximal Function Estimates

Author(s): Simon Bortz, Steve Hofmann, José Luis Luna Garcia, Svitlana Mayboroda, Bruno Poggi
Published in: Archive for Rational Mechanics and Analysis, Issue 248, 2024, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-024-01977-x

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

Author(s): Alejandro Molero; Mihalis Mourgoglou; Carmelo Puliatti; Xavier Tolsa
Published in: Archive for Rational Mechanics and Analysis, 2023, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-023-01852-1

Non-peer reviewed articles (1)

Connectivity conditions and boundary Poincaré inequalities

Author(s): Tapiola, Olli; Tolsa, Xavier
Published in: Analysis & PDE, 2023, Page(s) Accepted for publication, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.48550/arxiv.2205.11667

Book chapters (1)

Carleson’s $$\varepsilon ^2$$ Conjecture in Higher Dimensions and Faber-Krahn Inequalities

Author(s): Xavier Tolsa
Published in: Trends in Mathematics, Recent Developments in Fractals and Related Fields, 2025, Page(s) 373-392
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-80453-3_14