Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Semilinear partial differential equations involving nonlocal operators and Borel measures

2017/25/B/ST1/00878

Keywords:

Dirichlet operator semilinear PDEs Dirichlet problem reduced measures obstacle problem Martin's kernel,fractional Laplacian Feynman-Kac formula Hunt process Kato's inequality renormalized solution

Descriptors:

  • ST1_11:
  • ST1_13:

Panel:

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

Host institution :

Uniwersytet Mikołaja Kopernika w Toruniu, Wydział Matematyki i Informatyki

woj. kujawsko-pomorskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Tomasz Klimsiak 

Number of co-investigators in the project: 1

Call: OPUS 13 - announced on 2017-03-15

Amount awarded: 175 000 PLN

Project start date (Y-m-d): 2018-01-24

Project end date (Y-m-d): 2023-01-23

Project duration:: 60 months (the same as in the proposal)

Project status: Project settled

Project description

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

Information in the final report

  • Publication in academic press/journals (11)
  1. Nonlinear BSDEs with two optional Doob's class barriers satisfying weak Mokobodzki's condition and extended Dynkin games.
    Authors:
    Tomasz Klimsiak, Maurycy Rzymowski
    Academic press:
    Applied Mathematics and Optimization (rok: 2023, tom: vol 88 no. 3, Paper No. 80, 33 pp., strony: 33 pp.), Wydawca: Springer
    Status:
    Published
    DOI:
    brak - link to the publication
  2. ASYMPTOTICS FOR LOGISTIC-TYPE EQUATIONS WITH DIRICHLET FRACTIONAL LAPLACE OPERATOR
    Authors:
    Tomasz Klimsiak
    Academic press:
    Advances in Differential Equations (rok: 2023, tom: Volume 28, Numbers 3-4, strony: 169-216), Wydawca: Khayyam Publishing, Inc.
    Status:
    Published
    DOI:
    brak - link to the publication
  3. On the maximum principles and the quantitative version of the Hopf lemma for uniformly elliptic integro-differential operators
    Authors:
    Tomasz Klimsiak, Tomasz Komorowski
    Academic press:
    Journal of Differential Equations (rok: 2021, tom: 298, strony: 346-386), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2021.07.008 - link to the publication
  4. Dirichlet problem for semilinear partial integro-differential equations: the method of orthogonal projection
    Authors:
    Tomasz Klimsiak, Andrzej Rozkosz
    Academic press:
    J. Eur. Math. Soc. , Wydawca: European Mathematical Society Press
    Status:
    Submitted
    DOI:
    brak - link to the publication
  5. Location of zeros of non-trivial positive supersolutions to Schrodinger equations
    Authors:
    Tomasz Klimsiak
    Academic press:
    Mathematische Annalen , Wydawca: Springer
    Status:
    Submitted
    DOI:
    brak - link to the publication
  6. Nonlinear elliptic equations with integro-differential divergence form operators and measure data under sign condition on the nonlinearity
    Authors:
    Tomasz Klimsiak
    Academic press:
    Communications in Contemporary Mathematics , Wydawca: World Scientific
    Status:
    Submitted
    DOI:
    brak - link to the publication
  7. Schrodinger equations with smooth measure potential and general measure data
    Authors:
    Tomasz Klimsiak
    Academic press:
    Nonlinear Analysis (rok: 2022, tom: 218, strony: Paper No. 112774), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.na.2021.112774 - link to the publication
  8. On uniqueness and structure of renormalized solutions to integro-differential equations with general measure data
    Authors:
    Tomasz Klimsiak
    Academic press:
    Nonlinear Differential Equations and Applications NoDEA (rok: 2020, tom: 1,15763888888889, strony: 24), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-020-00650-y - link to the publication
  9. Hopf type lemmas for subsolutions of integro-differential equations
    Authors:
    Tomasz Klimsiak, Tomasz Komorowski
    Academic press:
    Bernoulli (rok: 2023, tom: 29, strony: 1435–1463), Wydawca: Bernoulli Society
    Status:
    Published
    DOI:
    10.3150/22-BEJ1505 - link to the publication
  10. Uniqueness for an obstacle problem arising from logistic-type equations with fractional Laplacian
    Authors:
    Tomasz Klimsiak
    Academic press:
    Potential Analysis (rok: 2023, tom: vol. 59 no. 3, strony: 897–916), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-022-09986-9 - link to the publication
  11. A priori estimates for multidimensional BSDEs with integrable data
    Authors:
    Tomasz Klimsiak, Maurycy Rzymowski
    Academic press:
    Electronic Communications in Probability , Wydawca: Institute of Mathematical Statistics and Bernoulli Society
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication

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