Research
My scientific work is based on studing partial differential equations using
theory and techniques of real and functional analysis such as Fourier analysis,
microlocal defect functionals (H-measures, semiclassical measures...) and strongly
continuous semigroups.
I am part of a research project (funded by CSF) Analysis of partial differential equations and shape optimization, and an active
member of Seminar
for differential equations and numerical analysis at the Department of Mathematics, University
of Zagreb.
Currantly, I am an associate professor at Department of Mathematics, Faculty of Science, University of Zagreb.
Submitted
Published (or accepted for publishing)
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Marko Erceg, Sandeep Kumar Soni:
The von Neumann extension theory for abstract Friedrichs operators,
Zeitschrift für Analysis und ihre Anwendungen, accepted for publication, 21 pp.
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[preprint] |
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Krešimir Burazin, Marko Erceg, Marcus Waurick:
Evolutionary equations are G-compact,
Journal of Evolution Equations,
24, Article number: 45 (2024) 20 pp.
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Nenad Antonić, Marko Erceg:
One-scale H-distributions and variants,
Results in Mathematics,
78, Article number: 165 (2023) 53 pp.
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[preprint] |
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Marko Erceg, Marin Mišur,
Darko Mitrović:
Velocity averaging for diffusive transport equations with discontinuous flux,
Journal of the London Mathematical Society,
107 (2023) 658-703.
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[preprint] |
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Marko Erceg, Sandeep Kumar Soni:
Classification of classical Friedrichs differential operators: One-dimensional scalar case,
Communications on Pure and Applied Analysis,
21 (2022) 3499-3527.
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[preprint] |
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Marko Erceg, Darko Mitrović:
Strong traces to degenerate parabolic equations,
SIAM Journal on Mathematical Analysis,
54 (2022) 1775-1796.
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Nenad Antonić, Marko Erceg, Marin Mišur:
Distributions of anisotropic order and applications to H-distributions,
Analysis and Applications,
19 (2021) 801-843. |
[preprint] |
| ) |
Marko Erceg, Alessandro Michelangeli:
On contact interactions realised as Friedrichs systems,
Complex Analysis and Operator Theory,
13 (2019) 703-736. |
[preprint] |
| ) |
Marko Erceg, Martin Lazar:
Characteristic
scales of bounded L2 sequences, Asymptotic Analysis,
109(3-4) (2018) 171-192. |
[preprint] |
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Marko Erceg, Ivan Ivec:
Second
commutation lemma for fractional H-measures,
Journal of Pseudo-Differential Operators and Applications,
9(3) (2018) 589-613. |
[preprint] |
| ) |
Nenad Antonić,
Krešimir Burazin,
Ivana Crnjac, Marko Erceg:
Complex Friedrichs systems and applications,
Journal of Mathematical Physics,
58 (2017) 101508, 22 pp. |
[preprint] |
| ) |
Nenad Antonić, Marko Erceg,
Alessandro Michelangeli:
Friedrichs
systems in a Hilbert space framework: solvability and multiplicity,
Journal of Differential Equations,
263 (2017) 8264-8294. |
[preprint] |
| ) |
Marko Erceg, Ivan Ivec:
On generalisation of
H-measures, Filomat,
31(16) (2017) 5027-5044. |
[preprint] |
| ) |
Nenad Antonić, Marko Erceg,
Martin Lazar:
Localisation principle for one-scale H-measures,
Journal of Functional Analysis,
272 (2017) 3410-3454. |
[preprint] |
| ) |
Krešimir Burazin, Marko Erceg:
Non-stationary abstract Friedrichs systems,
Mediterranean Journal of Mathematics,
13 (2016) 3777-3796. |
[preprint]
|
| ) |
Krešimir Burazin, Marko Erceg:
Estimates for mild
solutions to semilinear Cauchy problems,
Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 194, pp. 1-10. |
[preprint] |
Thesis
