Microlocal defect tools in partial differential equations

Dissemination

Talks at conferences

1. Marko Erceg (with Nenad Antonić and Alessandro Michelangeli): Friedrichs operators and dual pairs, lecture at GAMM annual meeting, Vienna, 18-22 February 2019. [link]
2. Nenad Antonić (with Marko Erceg and Marin Mišur): H-distributions and variants, lecture at ISAAC 2019 Congress, Aveiro, 29 July 2019 [link]
3. Ivan Ivec (with Nenad Antonić and Ivana Vojnović): Continuity of linear operators on mixed-norm Lebesgue and Sobolev spaces, lecture at ISAAC 2019 Congress, Aveiro, 29 July 2019 [link]
4. Nenad Antonić (with Krešimir Burazin and Jelena Jankov): Small-amplitude homogenisation of Kirchhoff-Love plate, lecture at 6th Najman conference, Sv. Martin na Muri, 9 September 2019 [link]
5. Ivana Vojnović: Application of defect distributions to equations with polynomial coefficients, lecture at 6th Najman conference, Sv. Martin na Muri, 9 September 2019 [link]
6. Ivan Ivec (with Ivana Vojnović): H-distributions on Hörmander spaces, lecture at Workshop Microlocal analysis and partial differential equations, Zagreb, 26 February 2020 [link]
7. Ivana Vojnović: Defect distributions applied to differential equations with power function type coefficients, lecture at Workshop Microlocal analysis and partial differential equations, Zagreb, 26 February 2020 [link]
8. Nenad Antonić: H-measures and propagation of microlocal energy density, lecture at Tenth Conference on Applied Mathematics and Scientific Computing, Brijuni, 15 September 2020 [link]
9. Nenad Antonić (with Marko Erceg and Eduard Nigsch): H-distributions with a characteristic length, lecture at Microlocal and Time-Frequency Analysis, Virtual days, 22 June 2021 [link]
10. Nenad Antonić (with Marko Erceg): One-scale H-measures and H-distributions, lecture at Brijuni Applied Mathematics Workshop 2021, Brijuni, 6 July 2021 [link]
11. Ivana Vojnović (with Nevena Dugandžija): Singular solution of the Hartree equation with a delta potential, lecture at Brijuni Applied Mathematics Workshop, Brijuni, 6 July 2021 [link]
12. Ivan Ivec (with Ivana Vojnović): Basic calculus of pseudodifferential operators with nonsmooth symbols, lecture at ISAAC 2021 Congress, Ghent, 2-6 August 2021 [link]
13. Nenad Antonić (with Marko Erceg, Krešimir Burazin and Jelena Jankov): Microlocal defect functionals and applications, lecture at Time-frequency representations for function spaces, Novi Sad, 13 April 2022 [link]
14. Ivan Ivec (with Nenad Antonić and Ivana Vojnović): Continuity of pseudodifferential operators with nonsmooth symbols on mixed-norm Lebesgue spaces, lecture at Time-frequency representations for function spaces, Novi Sad, 13 April 2022 [link]
15. Marko Erceg (with Krešimir Burazin Mišur and Miłosz Krupski): Homogenisation of nonlocal linear elliptic operators, lecture at 7th Croatian Mathematical Congress, Split, 15 June 2022. [link]
16. Sandeep Kumar Soni (with Marko Erceg): Classical Friedrichs operators in one dimensional scalar case, lecture at 7th Croatian Mathematical Congress, Split, 15 June 2022. [link]
17. Ivana Vojnović: H-distributions related to Hörmander spaces, lecture at Analysis, PDEs and Applications (celebrating 60th anniversary of professor Nenad Antonić), Dubrovnik, 19-25 June 2022. [link]
18. Miłosz Krupski: Degenerate nonlocal Fokker-Planck equations, lecture at Analysis, PDEs and Applications (celebrating 60th anniversary of professor Nenad Antonić), Dubrovnik, 19-25 June 2022. [link]
19. Sandeep Kumar Soni (with Marko Erceg): The graph space of abstract Friedrichs operators, lecture at Analysis, PDEs and Applications (celebrating 60th anniversary of professor Nenad Antonić), Dubrovnik, 19-25 June 2022. [link]
20. Marko Erceg (with Darko Mitrović): Strong traces of entropy solutions to degenerate parabolic equations on the boundary, lecture at 11th Conference on Applied Mathematics and Scientific Computing, Brijuni, 8 September 2022 [link]
21. Nenad Antonić: Localisation principle for microlocal defect functionals and small-amplitude homogenisation, lecture at 11th Conference on Applied Mathematics and Scientific Computing, Brijuni, 9 September 2022 [link]
22. Ivan Ivec (with Nenad Antonić and Ivana Vojnović): Bounded operators on mixed-norm Lebesgue spaces, lecture at IWOTA 2022, Kraków, 6-10 September 2022 [link]
23. Miłosz Krupski: Fully nonlinear mean field games, lecture at International Conference on Generalized Functions GF2022, Wien, 20 September 2022 [link]
24. Nenad Antonić: Homogenisation and microlocal energy propagation for the wave equation revisited, lecture at International Conference on Generalized Functions GF2022, Wien, 21 September 2022 [link]
25. Sandeep Kumar Soni (with Marko Erceg): Abstract Friedrichs operators and skew self-adjoint realisations, lecture at 7th Najman conference on spectral theory and differential equations, Brijuni, 18-23 September 2023. [link]

Lectures and seminars

1. Marko Erceg (with Nenad Antonić): One-scale H-distributions, seminar at Department of Mathematics, University of Vienna, 23 November 2018. [link]
2. Nenad Antonić (with Marko Erceg, Martin Lazar and Marko Vrdoljak): Parabolic H-measures and applications in continuum mechanics, at Departamento de Ingeniería Estructural y Geotécnica, Pontificia Universidad Católica de Chile, Santiago, 30 April 2019 [link]
3. Nenad Antonić (with Marko Erceg, Ivan Ivec, Marin Mišur and Darko Mitrović): Microlocal defect functionals: H-distributions, at Instituto de Ingeniería Matemática y Computacional, Pontificia Universidad Católica de Chile, Santiago, 6 May 2019 [link]
4. Nenad Antonić: Mikrolokalni defektni functionali, at Mathematical Coloquium, Department of Mathematics, University J. J. Strossmayer, Osijek, 5 March 2020 [link]
5. Matko Grbac: Gabor wave front sets and propagation of singularities, at Seminar for differential equations and numerical analysis, Zagreb, 6 December 2021
6. Sandeep Kumar Soni (with Marko Erceg): Abstract Friedrichs operators and the graph space, at Seminar for differential equations and numerical analysis, Zagreb, 24 January 2022 [link]
7. Sandeep Kumar Soni (with Marko Erceg): Classification of classical Friedrichs differential operators: One dimensional scalar case, at Seminar for differential equations and numerical analysis, Zagreb, 7 February 2022 [link]
8. Marko Erceg (with Marin Mišur and Darko Mitrović): Entropy solutions of degenerate parabolic equations, lecture at Mathematical Colloquium, Osijek, 17 March 2022. [link]
9. Sandeep Kumar Soni: Fundamental solutions of linear partial differential operators with constant coefficients, at Seminar for differential equations and numerical analysis, Zagreb, 6 June 2022 [link]
10. Marko Erceg (with Darko Mitrović): Entropy solutions of degenerate parabolic equations: existence and strong traces, lecture at Applied Mathematics Seminar, UNC Greensboro, 21 November 2022. [link]
11. Sandeep Kumar Soni: Classification of boundary conditions for Friedrichs systems, at Seminar for differential equations and numerical analysis, Zagreb, 29 November 2022 [link]

Posters

Sandeep Kumar Soni (with Marko Erceg): Abstract Friedrichs Operators, poster presentation at the Summer School “Heat Kernels and Spectral Geometry: From Manifolds to Graphs”, Bregenz, 28 August - 3 September 2022 [link]

Ivana Vojnović: Generalised solutions to linear and non-linear Schrödinger-type equations, poster presentation at 11th Conference on Applied Mathematics and Scientific Computing, Brijuni, 9 September 2022 [link]

Matko Grbac: Asymptotic behaviour of solutions to the wave equation with variable coefficients, poster presentation at 11th Conference on Applied Mathematics and Scientific Computing, Brijuni, 9 September 2022 [link]

Sandeep Kumar Soni (with Marko Erceg): The Graph Space of Abstract Friedrichs Operators and Classification of Classical Friedrichs Operators in 1-D Scalar Case, poster presentation at the Summer School on Analysis and Applied Mathematics, Münster, 12-16 September 2022 [link]

Sandeep Kumar Soni (with Marko Erceg): Classical Friedrichs Operators in 1-D Scalar Case, poster presentation at the Summer School on Horizons in non-linear PDEs, Ulm, 26-30 September 2022 [link]

Visitors

1. Eduard Nigsch, Department of Mathematics, University of Vienna, 4-7 November 2018, lecture at Seminar for differential equations and numerical analysis:
   Laplace transformation of vector-valued distributions and applications to Cauchy-Dirichlet problems
2. James Vickers, University of Southampton, 4-8 February 2019, lecture at Seminar for differential equations and numerical analysis:
   Using methods from numerical analysis to prove well-posedness of low regularity PDEs
3. Michael Kunzinger, Department of Mathematics, University of Vienna, 5-8 February 2019
4. Noè Caruso, SISSA, Trieste, 25-29 June 2019, lecture at Seminar for differential equations and numerical analysis:
   On Krylov subspace methods and solutions to infinite-dimensional inverse linear problems
5. Sandro Coriasco, Università di Torino, 24 February 2020, lecture at Seminar for differential equations and numerical analysis:
   Group properties of pseudo-differential operators and their applications
6. Miłosz Krupski, University of Wroclaw, 31 January 2022, lecture at Seminar for differential equations and numerical analysis:
   A framework for nonlocal, nonlinear diffusions
7. Francois Murat,
12. Irfan Glogić, University of Vienna, 12-15 March 2023, lecture at Seminar for differential equations and numerical analysis:
    Stability of self-similar blowup for the wave maps equation