Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Anisotropic least gradient problem

2017/27/N/ST1/02418

Keywords:

least gradient problem anisotropy calculus of variations singular PDEs

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_17: Applied mathematics

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Warszawski, Wydział Matematyki, Informatyki i Mechaniki

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Wojciech Górny 

Number of co-investigators in the project: 2

Call: PRELUDIUM 14 - announced on 2017-09-15

Amount awarded: 106 400 PLN

Project start date (Y-m-d): 2018-07-17

Project end date (Y-m-d): 2022-10-16

Project duration:: 51 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. Zestaw komputera stacjonarnego z monitorem i potrzebnym wyposażeniem (7 000 PLN)

Information in the final report

  • Publication in academic press/journals (15)
  • Articles in post-conference publications (1)
  1. Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents
    Authors:
    Wojciech Górny
    Academic press:
    Journal of Geometric Analysis (rok: 2022, tom: 32, strony: 128), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12220-021-00861-4 - link to the publication
  2. Least gradient functions in metric random walk spaces
    Authors:
    Wojciech Górny, José M. Mazón
    Academic press:
    ESAIM: Control, Optimisation and Calculus of Variations (rok: 2021, tom: 27, strony: S28), Wydawca: EDP Sciences
    Status:
    Published
    DOI:
    10.1051/cocv/2020087 - link to the publication
  3. The Neumann and Dirichlet problems for the total variation flow in metric measure spaces
    Authors:
    Wojciech Górny, José M. Mazón
    Academic press:
    Advances in Calculus of Variations (rok: 2022, tom: ahead of print, strony: -), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/acv-2021-0107 - link to the publication
  4. The trace space of anisotropic least gradient functions depends on the anisotropy
    Authors:
    Wojciech Górny
    Academic press:
    Mathematische Annalen (rok: 2022, tom: ahead of print, strony: -), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00208-022-02488-4 - link to the publication
  5. L^p regularity of least gradient functions
    Authors:
    Wojciech Górny
    Academic press:
    Proceedings of the American Mathematical Society (rok: 2020, tom: 148 (7), strony: 3009-3019), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/15031 - link to the publication
  6. Least gradient problem on annuli
    Authors:
    Samer Dweik, Wojciech Górny
    Academic press:
    Analysis & PDE (rok: 2022, tom: 15, strony: 699-725), Wydawca: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2022.15.699 - link to the publication
  7. Local and nonlocal 1-Laplacian in Carnot groups
    Authors:
    Wojciech Górny
    Academic press:
    Annales Academiae Scientiarum Fennicae Mathematica (rok: 2022, tom: 47, strony: 427-456), Wydawca: Academia Scientiarum Fennica
    Status:
    Published
    DOI:
    10.54330/afm.114742 - link to the publication
  8. On the p-Laplacian evolution equation in metric measure spaces
    Authors:
    Wojciech Górny, José M. Mazón
    Academic press:
    Journal of Functional Analysis (rok: 2022, tom: 283, strony: 109621), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2022.109621 - link to the publication
  9. Applications of optimal transport methods in the least gradient problem
    Authors:
    Wojciech Górny
    Academic press:
    Annali della Scuola Normale Superiore di Pisa - Classe di Scienze , Wydawca: Scuola Normale Superiore
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  10. Optimal transport approach to Sobolev regularity of solutions to the weighted least gradient problem
    Authors:
    Samer Dweik, Wojciech Górny
    Academic press:
    SIAM Journal on Mathematical Analysis , Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  11. Least gradient problem with Dirichlet condition imposed on a part of the boundary
    Authors:
    Wojciech Górny
    Academic press:
    Calculus of Variations and Partial Differential Equations , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  12. Least gradient problem with respect to a non-strictly convex norm
    Authors:
    Wojciech Górny
    Academic press:
    Nonlinear Analysis (rok: 2020, tom: 200, strony: 112049), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.na.2020.112049 - link to the publication
  13. Existence of minimisers in the least gradient problem for general boundary data
    Authors:
    Wojciech Górny
    Academic press:
    Indiana University Mathematics Journal (rok: 2021, tom: 70, strony: 1003–1037), Wydawca: Indiana University
    Status:
    Published
    DOI:
    10.1512/iumj.2021.70.8420 - link to the publication
  14. The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces
    Authors:
    Wojciech Górny, José M. Mazón
    Academic press:
    Communications in Contemporary Mathematics , Wydawca: World Scientific
    Status:
    Submitted
    DOI:
    brak - link to the publication
  15. The double-bubble problem on the square lattice
    Authors:
    Manuel Friedrich, Wojciech Górny, Ulisse Stefanelli
    Academic press:
    Transactions of the Americal Mathematical Society , Wydawca: American Mathematical Society
    Status:
    Submitted
    DOI:
    brak - link to the publication
  1. Weak solutions to gradient flows in metric measure spaces
    Authors:
    Wojciech Górny, José M. Mazón
    Conference:
    92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (rok: 2022, ), Wydawca: Wiley
    Data:
    konferencja 15.08-19.08
    Status:
    Accepted for publication

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