Gyula Csató

Associate Professor

Universitat de Barcelona, Facultat de Matemàtiques i Informàtica, Gran Via de les Corts Catalanes, 585, 08007, Barcelona, Spain

+34934021631

and Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, 08193 Bellaterrra, Spain.

Research interests

General: partial differential equations, calculus of variations, differential geometry.

In particular: differential forms, first order boundary value problems, pullback equation, Jacobian equation, divergence equation, isoperimetric problems, rearrangements and symmetry, analysis on manifolds, Moser-Trudinger inequalities, non-local operators, fractional mean curvature

Curriculum vitae (pdf)

Publications and preprints

19. Csató G., Mas A., Strict Rearrangement Inequalities: Nonexpansivity and Periodic Gagliardo Semi-Norms, preprint in preparation
18. Cabré X., Csató G., Mas A., Periodic Solutions to Integro-Differential Equations: Variational Formulation, symmetry, and regularity, arXiv link to pdf .
17. Cabré X., Csató G., Mas A., On the stability of cylinders as periodic-nonlocal CMC surfaces, preprint.
16. Cabré X., Csató G., Mas A., Existence and symmetry of periodic nonlocal-CMC surfaces via variational methods, to appear in Journal für reine und angewandte Mathematik, arxiv link to pdf
15. Cabré X., Cozzi M. and Csató G., A fractional Michael-Simon Sobolev inequality on convex hypersurfaces, to apper in Ann. Inst. H. Poincaré Anal. Non Lineaire, pdf.
14. Chowdhury I., Csató G., Firoz S. and Roy P., Study of fractional Poincaré inequalities on some unbounded domains, to appear in Discrete Continuous Dynam. Syst., pdf.
13. Csató G., Roy P. and V.H. Nguyen, Extremals for the Singular Moser-Trudinger Inequality via n-Harmonic Transplantation, to appear in J. Diff. Equations, pdf
12. Bousquet P. and Csató G., The equation div u + <a; u> = f , to appear in Comm. in Contemporary Math., pdf
11. Csató G., Kneuss O. and Rajendran D., On the boundary conditions in estimating nabla w by div w and curl w , to appear in Proc. Roy. Soc. Edinburgh Sect. A , https://doi.org/10.1017/prm.2018.48, pdf
10. Csató G., Dacorogna B. and Sil S., On the best constant in Gaffney inequality, J. Funct. Anal. , 274 (2018), no. 2, 461-503, pdf
9. Csató G., On the isoperimetric problem with perimeter density rp; Comm. on Pure and Applied Analysis , Volume 17, Issue 6 (2018) 2729-2749, pdf
8. Csató G. and Roy P., The singular Moser-Trudinger inequality on simply connected domains, Communications in Partial Dierential Equations , 41 (2016), no. 5, 838-847, pdf
7. Csató G. and Roy P., Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions, Calc. Var. Partial Dierential Equations , 54 , Issue 2 (2015), 2341-2366, pdf
6. Csató G., An isoperimetric problem with density and the Hardy-Sobolev inequality in R2 , Differential Integral Equations , 28 , Number 9/10 (2015), 971-988, pdf
5. Csató G. and Dacorogna B., A Dirichlet problem involving the divergence operator, Ann. Inst. H. Poincaré Anal. Non Lineaire , 33 (2016), no. 3, 829-848, pdf
4. Csató G., Dacorogna B. and Kneuss O., The second order pullback equation Calc. Var. Partial Dierential Equations , 49 (2014), 583-611, pdf
3. Csató G., On an integral formula for dierential forms and its applications on manifolds with boundary, Analysis , 33 (2013), 349-366, pdf
2. Csató G., Dacorogna B. and Kneuss O., The pullback equation for differential form , Birkhauser/Springer, New York, 2012. (book) http://www.springer.com/la/book/9780817683122
1. Csató G. and Dacorogna B., An identity involving exterior derivatives and applications to Gaffney inequality, Discrete Continuous Dynam. Syst., Series S , 5 (2012), 531-544, pdf

Thesis (EPFL 2012), title "Some boundary value problems involving differential forms", download here pdf. Contains some results of the book "The pullback equation for differential forms" written in much more detail.

Video of my talk (on fractional Michael-Simon Sobolev inequality): see link to youtube video here (see here for abstract )

Science divulgation activity/outreach of my research: see this video

Links to some recent and upcoming conferences and workshops (member or organizing committee)

JISD 2024 (Summer school on interaction between dynamical systems and partial differential equations)
JISD 2021/2022 www.crm.cat/jisd2022/ (JISD past events: www.crm.cat/jisd-past-editions/ )
JISD 2023 https://www.crm.cat/jisd-2023/
BMS-BGSMath Junior meeting bgsmath.cat/event/bms-bgsmath-junior-meeting-2022/