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Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Analysis of nonlocal operators

2014/14/M/ST1/00600

Keywords:

nonlocal operator trace operator unimodal semigroup Markov process Harnack inequality heat kernel parametrix anisotropy

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_13: Probability and statistics
  • ST1_9: Operator algebras and functional 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, Wydział Matematyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Krzysztof Bogdan 

Number of co-investigators in the project: 9

Call: HARMONIA 6 - announced on 2014-06-16

Amount awarded: 696 800 PLN

Project start date (Y-m-d): 2015-05-06

Project end date (Y-m-d): 2018-11-05

Project duration:: 42 months (the same as in the proposal)

Project status: Project settled

Information in the final report

  • Publication in academic press/journals (19)
  • Book publications / chapters in book publications (1)
  1. Estimates of Dirichlet heat kernel for symmetric Markov processes
    Authors:
    Tomasz Grzywny, Kyung-Youn Kim, Panki Kim
    Academic press:
    Stochastic Processes and their Applications (rok: 2020, tom: 130, strony: 431-470), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2019.03.017 - link to the publication
  2. On certain variant of strongly nonlinear multidimensional interpolation inequality
    Authors:
    Tomasz Choczewski, Agnieszka Kałamajska
    Academic press:
    Topological Methods in Nonlinear Analysis (rok: 2018, tom: 52(1), strony: 49-67), Wydawca: Juliusz Schauder University Centre for Nonlinear Studies
    Status:
    Published
    DOI:
    10.12775/TMNA.2017.050 - link to the publication
  3. Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes
    Authors:
    Tomasz Grzywny, Mateusz Kwaśnicki
    Academic press:
    Stochastic Processes and their Applications (rok: 2018, tom: 128, strony: 13881), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.spa.2017.04.004 - link to the publication
  4. Weak and Young measure solutions for hyperbolic initial boundary value problems of elastodynamics in the Orlicz-Sobolev space setting
    Authors:
    Hong Thai Nguyen, Dariusz Pączka
    Academic press:
    SIAM Journal on Mathematical Analysis (rok: 2016, tom: 48, strony: 1297–1331), Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/15M1016138 - link to the publication
  5. Extension and trace for nonlocal operators
    Authors:
    Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba, Artur Rutkowski
    Academic press:
    Journal de Mathématiques Pures et Appliquée (rok: 2019, ), Wydawca: Elsevier
    Status:
    Accepted for publication
    DOI:
    10.1016/j.matpur.2019.09.005 - link to the publication
  6. Remarks on the nonlocal Dirichlet problem
    Authors:
    Tomasz Grzywny, Moritz Kassmann, Łukasz Leżaj
    Academic press:
    Potential Analysis (rok: 2019, ), Wydawca: Springer
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  7. Intrinsic compound kernel estimates for the transition probability density of Lévy-type processes and their applications
    Authors:
    Victoria Knopova, Aleksei Kulik
    Academic press:
    Probability and Mathematical Statistics (rok: 2017, tom: 37, strony: 53–100), Wydawca: Wydawn. Uniw. Wrocław.
    Status:
    Published
    DOI:
    10.19195/0208-4147.37.1.3 - link to the publication
  8. Strongly nonlinear Gagliardo–Nirenberg inequality in Orlicz spaces and Boyd indices
    Authors:
    Claudia Capone, Alberto Fiorenza, Agnieszka Kałamajska
    Academic press:
    Rendiconti Lincei - Matematica e Applicazioni (rok: 2017, tom: 28, strony: 119-141), Wydawca: European Mathematical Society Publishing House
    Status:
    Published
    DOI:
    10.4171/RLM/755 - link to the publication
  9. Semilinear Dirichlet problem for the fractional Laplacian
    Authors:
    Krzysztof Bogdan, Sven Jarohs, Edyta Kania
    Academic press:
    Nonlinear Analysis (rok: 2019, ), Wydawca: Elsevier
    Status:
    Accepted for publication
    DOI:
    10.1016/j.na.2019.04.011 - link to the publication
  10. Transition density estimates for relativistic $\alpha$-stable processes on metric spaces
    Authors:
    Hubert Balsam, Katarzyna Pietruska-Pałuba
    Academic press:
    Probability and Mathematical Statistics (rok: 2019, ), Wydawca: Wydawn. Uniw. Wrocław.
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  11. On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems
    Authors:
    Tomasz Choczewski, Agnieszka Kałamajska
    Academic press:
    Rendiconti Lincei - Matematica e Applicazioni (rok: 2019, tom: 30, strony: 479-496), Wydawca: European Mathematical Society
    Status:
    Published
    DOI:
    10.4171/RLM/856 - link to the publication
  12. The Dirichlet problem for nonlocal Lévy-type operators
    Authors:
    Artur Rutkowski
    Academic press:
    Publicacions Matemàtiques (rok: 2018, tom: 62, strony: 213-251), Wydawca: Department of Mathematics of the Universitat Autònoma de Barcelona
    Status:
    Published
    DOI:
    10.5565/PUBLMAT6211811 - link to the publication
  13. Yaglom limit for stable processes in cones
    Authors:
    Krzysztof Bogdan, Zbigniew Palmowski, Longmin Wang
    Academic press:
    Electronic Journal of Probability (rok: 2018, tom: 23, strony: 45310), Wydawca: Institute of Mathematical Statistics
    Status:
    Published
    DOI:
    10.1214/18-EJP133 - link to the publication
  14. Heat kernel of anisotropic nonlocal operators
    Authors:
    Krzysztof Bogdan, Paweł Sztonyk, Victoria Knopova
    Academic press:
    Documenta Mathematica (rok: 2019, ), Wydawca: Deutsche Mathematiker-Vereinigung
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  15. Hitting Times of Points and Intervals for Symmetric Lévy Processes
    Authors:
    Tomasz Grzywny, Michał Ryznar
    Academic press:
    Potential Analysis (rok: 2017, tom: 46, strony: 739–777), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11118-016-9600-z - link to the publication
  16. On proper formulation of boundary condition for degenerated PDEs when trace embedding theorems are missing and application to nonhomogeneous BVPs
    Authors:
    Raj Narayan Dhara, Agnieszka Kałamajska
    Academic press:
    Complex Variables and Elliptic Equations (rok: 2016, tom: 61, strony: 1541-1553), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/17476933.2016.1174217 - link to the publication
  17. On solvability of nonlinear eigenvalue problems for degenerate PDEs of elliptic type
    Authors:
    Raj Narayan Dhara
    Academic press:
    Complex Variables and Elliptic Equations (rok: 2017, tom: 63, strony: 501-516), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/17476933.2017.1322075 - link to the publication
  18. Sharp Gaussian estimates for heat kernels of Schroedinger operators
    Authors:
    Krzysztof Bogdan, Jacek Dziubański and Karol Szczypkowski
    Academic press:
    Integral Equations and Operator Theory (rok: 2019, tom: 3,79375, strony: 20), Wydawca: Springer International Publishing
    Status:
    Published
    DOI:
    10.1007/s00020-019-2501-y - link to the publication
  19. 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 and Francis
    Status:
    Published
    DOI:
    10.1080/03605302.2018.1539102 - link to the publication
  1. A probabilistic proof of the breakdown of Besov regularity in L-shaped domains
    Authors:
    Victoria Knopova, René Schilling
    Book:
    Stochastic partial differential equations and related fields, Springer Proceedings in Mathematics & Statistics 229 (rok: 2018, tom: 229, strony: 473–488), Wydawca: Springer
    Status:
    Published

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