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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Inequalities and differential equations related to Markov operators

2015/18/E/ST1/00239

Keywords:

nonlocal operator nonlinear equation asymptotics of the solution unimodal process Green function heat kernel

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_13: Probability and statistics
  • ST1_8: Analysis

Panel:

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

Host institution :

Politechnika Wrocławska

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Tomasz Jakubowski 

Number of co-investigators in the project: 8

Call: SONATA BIS 5 - announced on 2015-06-15

Amount awarded: 1 034 500 PLN

Project start date (Y-m-d): 2016-04-28

Project end date (Y-m-d): 2022-04-27

Project duration:: 72 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. laptop (8 696 PLN)
  2. skaner (500 PLN)
  3. Laptop (2 szt.) (10 000 PLN)
  4. laptop (6 699 PLN)

Information in the final report

  • Publication in academic press/journals (31)
  1. Dirichlet heat kernel for the Laplacian in a ball
    Authors:
    Jacek Małecki, Grzegorz Serafin
    Academic press:
    Potential Analysis (rok: 2020, tom: 52, strony: 545-563), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-018-9750-2 - link to the publication
  2. Extension and trace for nonlocal operators
    Authors:
    K. Bogdan, T. Grzywny, K. Pietruska-Pałuba, A. Rutkowski
    Academic press:
    Journal de Mathématiques Pures et Appliquées (rok: 2020, tom: 137, strony: 33-69), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.matpur.2019.09.005 - link to the publication
  3. Fractional Laplacian with Hardy Potential
    Authors:
    Krzysztof Bogdan, Tomasz Grzywny, Tomasz Jakubowski, Dominika Pilarczyk
    Academic press:
    Communications in Partial Differential Equations (rok: 2019, tom: 44(1), strony: 20-50), Wydawca: TAYLOR & FRANCIS INC
    Status:
    Published
    DOI:
    10.1080/03605302.2018.1539102 - link to the publication
  4. Laplace Dirichlet heat kernels in convex domains
    Authors:
    G. Serafin
    Academic press:
    Journal of Differential Equations (rok: 2022, tom: 314, strony: 700-732), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.01.026 - link to the publication
  5. On density of compactly supported smooth functions in fractional Sobolev spaces
    Authors:
    B. Dyda, M. Kijaczko
    Academic press:
    Annali di Matematica Pura ed Applicata (rok: 2022, tom: 201, strony: 1855–1867), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10231-021-01181-8 - link to the publication
  6. On density of smooth functions in weighted fractional Sobolev spaces
    Authors:
    Bartłomiej Dyda, Michał Kijaczko
    Academic press:
    Nonlinear Analysis (rok: 2021, tom: 205, strony: 112231, 10 pp), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.na.2020.112231 - link to the publication
  7. Reduction of integration domain in Triebel-Lizorkin spaces
    Authors:
    A. Rutkowski
    Academic press:
    Studia Mathematica (rok: 2021, tom: 259 (2), strony: 121-152), Wydawca: Polska Akademia Nauk
    Status:
    Published
    DOI:
    10.4064/sm190729-14-5 - link to the publication
  8. Estimates of gradient of L-harmonic functions for nonlocal operators with order α > 1
    Authors:
    T. Grzywny, T. Jakubowski, G. Żurek
    Academic press:
    The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze , Wydawca: Scuola Normale Superiore
    Status:
    Submitted
    DOI:
    brak - link to the publication
  9. Relativistic stable operators with critical potentials
    Authors:
    Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
    Academic press:
    Analysis & PDE , Wydawca: Mathematical Sciences Publishers
    Status:
    Submitted
    DOI:
    brak - link to the publication
  10. Self-similar solution for Hardy operator
    Authors:
    K. Bogdan, T. Jakubowski, P. Kim, D. Pilarczyk
    Academic press:
    Archive for Rational Mechanics and Analysis , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  11. Optimal Hardy inequality for the fractional Laplacian on $L^p$
    Authors:
    K. Bogdan, T. Jakubowski, J. Lenczewska, K. Pietruska-Pałuba
    Academic press:
    Journal of Functional Analysis (rok: 2022, tom: 282, strony: 109395), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2022.109395 - link to the publication
  12. Feeling boundary by Brownian motion in a ball
    Authors:
    G. Serafin
    Academic press:
    Asymptotic Analysis , Wydawca: IOS Press
    Status:
    Accepted for publication
    DOI:
    10.3233/ASY-211734 - link to the publication
  13. Nonlinear nonlocal Douglas identity
    Authors:
    K. Bogdan, T. Grzywny, K. Pietruska-Pałuba, A. Rutkowski
    Academic press:
    Calculus of Variations and Partial Differential Equations , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  14. Berry-Esseen bounds for functionals of independent random variables
    Authors:
    N. Privault, G. Serafin
    Academic press:
    Electronic Journal of Probability (rok: 2022, tom: 27, strony: 13516), Wydawca: Institute of Mathematical Statistics and Bernoulli Society
    Status:
    Published
    DOI:
    10.1214/22-EJP795 - link to the publication
  15. Fractional Hardy-Sobolev type inequalities for half spaces and John domains
    Authors:
    Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
    Academic press:
    Proceedings of the American Mathematical Society (rok: 2018, tom: 146(8), strony: 3393-3402), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/proc/14051 - link to the publication
  16. Fractional Poincaré and localized Hardy inequalities on metric spaces
    Authors:
    B. Dyda, J. Lehrbäck, A. V. Vähäkangas
    Academic press:
    Advances in Calculus of Variations (rok: 2022, tom: xxx, strony: xxx), Wydawca: de Gruyter
    Status:
    Published
    DOI:
    10.1515/acv-2021-0069 - link to the publication
  17. Green function for gradient perturbation of unimodal Lévy processes in the real line
    Authors:
    Tomasz Grzywny, Tomasz Jakubowski, Grzegorz Żurek
    Academic press:
    Bulletin of the Malaysian Mathematical Sciences Society (rok: 2019, tom: 43, strony: 1223-1251), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40840-019-00738-4 - link to the publication
  18. Hyperbolic Green function estimates
    Authors:
    M. Ryznar, G. Serafin, T. Żak
    Academic press:
    Potential Analysis (rok: 2021, tom: 54, strony: 535-559), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-020-09837-5 - link to the publication
  19. Identities behind some congruences for r-Bell and derangement polynomials
    Authors:
    G. Serafin
    Academic press:
    Research in Number Theory (rok: 2020, tom: 6, strony: 14397), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s40993-020-00216-y - link to the publication
  20. Normal approximation for generalized U-statistics and weighted random graphs
    Authors:
    N. Privault, G. Serafin
    Academic press:
    Stochastics (rok: 2022, tom: 94 (3), strony: 432–458), Wydawca: Taylor&Francis
    Status:
    Published
    DOI:
    10.1080/17442508.2021.1959583 - link to the publication
  21. Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials
    Authors:
    Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski
    Academic press:
    Communications in Mathematical Physics , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  22. Fractional Burgers equation with singular initial condition
    Authors:
    T. Jakubowski, G. Serafin
    Academic press:
    Annales de l'Institut Henri Poincaré, Analyse Non Linéaire , Wydawca: EMS Press
    Status:
    Submitted
    DOI:
    brak - link to the publication
  23. Backward Touchard congruence
    Authors:
    G. Serafin
    Academic press:
    Bulletin of the Belgian Mathematical Society - Simon Stevin (rok: 2022, tom: 28 (4), strony: 603-614), Wydawca: The Belgian Mathematical Society
    Status:
    Published
    DOI:
    10.36045/j.bbms.210412a - link to the publication
  24. Heat kernel estimates of fractional Schrödinger operators with negative hardy potential
    Authors:
    T. Jakubowski, J. Wang
    Academic press:
    Potential Analysis (rok: 2020, tom: 53, strony: 997-1024), Wydawca: SPRINGER
    Status:
    Published
    DOI:
    10.1007/s11118-019-09795-7 - link to the publication
  25. Muckenhoupt A_p-properties of Distance Functions and Applications to Hardy-Sobolev-type Inequalities
    Authors:
    Bartłomiej Dyda, Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas
    Academic press:
    Potential Analysis (rok: 2019, tom: 50(1), strony: 83-105), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-017-9674-2 - link to the publication
  26. Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators
    Authors:
    K. Kaleta, R.L. Schilling
    Academic press:
    Journal of Functional Analysis (rok: 2020, tom: 279, strony: 108606), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2020.108606 - link to the publication
  27. Zero-energy bound state decay for nonlocal Schrödinger operators
    Authors:
    K. Kaleta, J. Lőrinczi
    Academic press:
    Communications in Mathematical Physics (rok: 2020, tom: 374, strony: 2151–2191), Wydawca: SPRINGER
    Status:
    Published
    DOI:
    10.1007/s00220-019-03515-3 - link to the publication
  28. Sharp and plain estimates for Schrödinger perturbation of Gaussian kernel
    Authors:
    T. Jakubowski, K. Szczypkowski
    Academic press:
    Journal d'Analyse Mathematique , Wydawca: Springer
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  29. Ground-state representation for fractional Laplacian on half-line
    Authors:
    Tomasz Jakubowski, Paweł Maciocha
    Academic press:
    Potential Analysis , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  30. Function spaces and extension results for nonlocal Dirichlet problems
    Authors:
    B. Dyda, M. Kassmann
    Academic press:
    Journal of Functional Analysis (rok: 2019, tom: 277, strony: 108134), Wydawca: ACADEMIC PRESS INC ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.024 - link to the publication
  31. Uniform pointwise asymptotics of solutions to quasi-geostrophic equation
    Authors:
    T. Jakubowski, G. Serafin
    Academic press:
    Nonlinearity (rok: 2020, tom: 33, strony: 2686-2706), Wydawca: IOP PUBLISHING LTD
    Status:
    Published
    DOI:
    10.1088/1361-6544/ab7637 - link to the publication

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